A259399 a(n) = Sum_{k=0..n} p(k)^2, where p(k) is the partition function A000041.
1, 2, 6, 15, 40, 89, 210, 435, 919, 1819, 3583, 6719, 12648, 22849, 41074, 72050, 125411, 213620, 361845, 601945, 995074, 1622338, 2626342, 4201367, 6681992, 10515756, 16449852, 25509952, 39333476, 60172701, 91577517, 138390481, 208096282, 310976731, 462512831
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..5000
Programs
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Maple
a:= proc(n) option remember; `if`(n<0, 0, combinat[numbpart](n)^2+a(n-1)) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 21 2018 -
Mathematica
Table[Sum[PartitionsP[k]^2,{k,0,n}],{n,0,50}]
Formula
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (16*sqrt(6)*Pi*n^(3/2)).
a(n) = 1 + A209536(n). - Alois P. Heinz, Oct 21 2018
Comments