A090982 a(n) = partitions(n)*partitions(n+1).
1, 2, 6, 15, 35, 77, 165, 330, 660, 1260, 2352, 4312, 7777, 13635, 23760, 40656, 68607, 114345, 188650, 307230, 496584, 793584, 1257510, 1976625, 3083850, 4769688, 7332360, 11191180, 16972670, 25582260, 38342568, 57123858, 84683907
Offset: 0
Examples
a(3)=15 because partitions(3)*partitions(4) = 3*5 = 15.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Maple
with(combinat): seq(numbpart(k)*numbpart(k+1), k=0..32) ; # Zerinvary Lajos, Jun 06 2007
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Mathematica
Table[PartitionsP[n + 1]*PartitionsP[n], {n, 0, 36}] Times@@@Partition[PartitionsP[Range[0,40]],2,1] (* Harvey P. Dale, May 23 2025 *) -
PARI
a(n)=numbpart(n)*numbpart(n+1) \\ Charles R Greathouse IV, Sep 02 2009
Formula
a(n) ~ exp(2*Pi*sqrt(2*n/3))/(48*n^2) * (1 + (11*Pi/(12*sqrt(6)) - sqrt(6)/Pi)/sqrt(n) + (3/(2*Pi^2) - 11/6 + 121*Pi^2/1728)/n). - Vaclav Kotesovec, Nov 04 2016