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G.f.: 1/(1-x)^4 * Product_{k>=1} (1 + x^k).
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%I #3 May 28 2019 07:38:43

%S 1,5,15,36,75,142,251,421,677,1052,1589,2343,3384,4800,6701,9224,

%T 12538,16850,22413,29534,38584,50010,64348,82238,104442,131864,165573,

%U 206830,257118,318176,392039,481082,588070,716216,869245,1051467,1267860,1524162,1826975

%N G.f.: 1/(1-x)^4 * Product_{k>=1} (1 + x^k).

%C In general, if g.f. = 1/(1-x)^m * Product_{k>=1} (1 + x^k), then a(n) ~ 2^(m - 2) * 3^(m/2 - 1/4) * n^(m/2 - 3/4) * exp(Pi*sqrt(n/3)) / Pi^m.

%F a(n) ~ 4 * 3^(7/4) * n^(5/4) * exp(Pi*sqrt(n/3)) / Pi^4.

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

%Y Cf. A000009, A014161, A036469, A095944, A120477, A292508, A325951.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, May 28 2019