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Apply partial sum operator 4 times to partition numbers.
4

%I #16 Feb 05 2022 15:19:10

%S 1,5,16,41,92,188,359,650,1128,1890,3075,4878,7571,11527,17254,25436,

%T 36988,53122,75435,106014,147573,203618,278657,378453,510344,683626,

%U 910031,1204301,1584896,2074841,2702765

%N Apply partial sum operator 4 times to partition numbers.

%C A014161 convolved with A010815 = the tetrahedral numbers: 1, 4, 10, 20, 35, ... . - _Gary W. Adamson_, Nov 09 2008

%H Vaclav Kotesovec, <a href="/A014161/b014161.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 3^(3/2)*n * exp(Pi*sqrt(2*n/3)) / Pi^4. - _Vaclav Kotesovec_, Oct 30 2015

%F G.f.: 1/(1-x)^4 * Product_{k>=1} 1/(1-x^k). - _Vaclav Kotesovec_, Oct 30 2015

%t nmax = 50; CoefficientList[Series[1/((1-x)^4 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 30 2015 *)

%Y Cf. A000041.

%Y Cf. A010815. - _Gary W. Adamson_, Nov 09 2008

%Y Column k=5 of A292508.

%K nonn

%O 0,2

%A _N. J. A. Sloane_