|
%I #18 Jan 21 2022 22:03:50
%S 1,2,6,15,35,77,165,330,660,1260,2352,4312,7777,13635,23760,40656,
%T 68607,114345,188650,307230,496584,793584,1257510,1976625,3083850,
%U 4769688,7332360,11191180,16972670,25582260,38342568,57123858,84683907
%N a(n) = partitions(n)*partitions(n+1).
%H G. C. Greubel, <a href="/A090982/b090982.txt">Table of n, a(n) for n = 0..1000</a>
%F 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
%e a(3)=15 because partitions(3)*partitions(4) = 3*5 = 15.
%p with(combinat): seq(numbpart(k)*numbpart(k+1), k=0..32) ; # _Zerinvary Lajos_, Jun 06 2007
%t Table[PartitionsP[n + 1]*PartitionsP[n], {n, 0, 36}]
%o (PARI) a(n)=numbpart(n)*numbpart(n+1) \\ _Charles R Greathouse IV_, Sep 02 2009
%Y Cf. A000041, A000070.
%K easy,nonn
%O 0,2
%A _Wouter Meeussen_, Feb 28 2004
|
