DATA FILES

  • Coefficients of Andrews spt-function
    spt(n) = the number of occurences of smallest parts in the partitions of n.
    For example, 
    Partitions of 4  Number of smallest parts
4                1
3+1              1
2+2              2
2+1+1            2
1+1+1+1          4
    spt(4)=1+1+2+2+4=10.
    FILES
    • sptcofs.txt
      Text file containing spt(n) for n=1 to n=10000.
      This file has 10000 lines one for each value of spt(n).
    • sptcofsmod2.txt
      Text file contains spt(n) mod 220 for n=1 to n=200000.
    • sptcofs.m
      This is a MAPLE m-file which contains the array sptcofs.
      EXAMPLE: 
      > read "sptcofs.m":
> sptcofs[5999];
   278941830700915838882974455560132543710354527039490199582717253860798628323895514520

> ifactor(%,easy);
                               3
                            (2)   (5)  (13)  (71)  (151) _c77_1
  • Partition function
    p(n) = the number of partitions of n.
    For example, p(4)=5 since there are 5 partitions of 4: 
    4
3+1
2+2
2+1+1
1+1+1+1

    FILES
    • ptncofs.txt
      Text file containing p(n) for n=1 to n=10000.
      This file has 10000 lines one for each value of p(n).
    • ptncofs.m
      This is a MAPLE m-file which contains the array ptncofs.
      EXAMPLE: 
      > read "ptncofs.m":
> ptncofs[5999];
4595772182112790143084312200387343025849540044362698346833677237664902997364019500

> ifactor(%,easy);
                            2     3
                         (2)   (5)   (13)  (353) _c76_1
  • Overpartition function
    pb(n) = the number of overpartitions of n.
    An overpartition is partition in which the first occurence of a part may be overlined. For example, pb(3)=8 since there are 8 overpartitions of 3: 
    3
3*
2+1
2+1*
2*+1
2*+1*
1+1+1
1*+1+1
    (Overline parts are marked by *).
    FILES
    • optncofs.txt
      Text file containing pb(n) for n=1 to n=10000.
      This file has 10000 lines one for each value of pb(n).
    • optncofs.m
      This is a MAPLE m-file which contains the array optncofs.
      EXAMPLE: 
      > read "optncofs.m":
> optncofs[1996];
              561516259751768382289813036527907885842788143179605073720

> ifactor(%,easy);                
                                3     7
                             (2)   (3)   (5)  (17) _c51_1
  • The Fishburn Numbers
    The Fishburn numbers xi(n) are defined by the formal power series 
                               oo                        
                          -----                     
                           \                        
                            )           n           
                           /     xi(n) q  = F(1 - q)
                          -----                     
                          n = 0                     
where                                              
                                   oo              
                                  -----           
                                   \              
                                    )             
                          F(q) =   /     (q, q)
                                  -----        n   
                                  n = 0
    See oeis.org/A022493.
    FILES
    • fishcofs.txt
      Text file containing xi(n) for n=0 to n=500.
      This file has 501 lines one for each value of xi(n).
    • fishcofs.m
      This is a MAPLE m-file which contains the array fishcofs.
      EXAMPLE: 
      > read "fishcofs.m":
> seq(fishcofs[j],j=0..10);
             1, 1, 2, 5, 15, 53, 217, 1014, 5335, 31240, 201608
> with(qseries):
> FISHGEN:=add(fishcofs[j]*q^j,j=0..500):
> findcong(FISHGEN,500);
                                  [3, 5, 5]
                                  [4, 5, 5]
                                  [6, 7, 7]
                                 [8, 11, 11]
                                 [9, 11, 11]
                                [10, 11, 11]
                                [16, 17, 17]
                                [17, 19, 19]
                                [18, 19, 19]
 {[3, 5, 5], [4, 5, 5], [6, 7, 7], [8, 11, 11], [9, 11, 11], [10, 11, 11], 

   [16, 17, 17], [17, 19, 19], [18, 19, 19]}
> fishcofs[499];

2041540377336862271213859295254324886316095045962006087397212630197321
6025717828916626588734439711670536972609795466338165650933183461403319
0452113737608168468298799543465301468790439285581649949999660559759105
6267250511758690788082972807169630797468437738392196362846571961118461
1111827535977816518064118759873205540133387049061210002985012204510408
9447841281138878318929507815014245267285520076642495312622941418256248
0031917329067116437918696480663779901357852971537787345898196183079574
3701544571822746943268232936793665500223423234752765265592045581896014
0743386635004919983674742353758663460385790293303237243610990472431040
5586446225550445712036228117355203759955173562943438424444977900503949
0718500531939165695922807647025462631159998831303002322738902757230487
2477106472423187802665733314010676048603528715558875468277182551486367
2390874860358557531726372555920101639600037677125936474504987391102775
1270057751770476250307879150074788095126290562042061493659572033163311
2789550393792974047528517110286306569109856375

> evalf(log(%)/log(10));
                                 1025.309958


> ifactor(fishcofs[499],easy);
                               3                    
                        (3) (5)  (13) (503) _c1019_1
  • Ramanujan's Mock Theta Functions

The url of this page is http://qseries.org/fgarvan/data/index.html.
Created by F.G. Garvan (fgarvan@math.ufl.edu) on Wednesday, June 24, 2009.
Last update made Wed Feb 6 20:48:03 EST 2019.

MAIL fgarvan@math.ufl.edu