A278668 - OEIS

%I #21 Nov 10 2017 05:19:00

%S 1,3,9,22,51,107,218,420,788,1428,2531,4375,7430,12377,20313,32833,

%T 52402,82585,128750,198588,303428,459375,689710,1027243,1518709,

%U 2229375,3251022,4710777,6785378,9717677,13841991,19614182,27656250,38810312,54216128,75406438

%N Expansion of Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^3 in powers of x.

%H Seiichi Manyama, <a href="/A278668/b278668.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^3.

%F a(n) ~ exp(2*Pi*sqrt(7*n/15)) * 7^(3/4) / (20 * 3^(3/4) * 5^(1/4) * n^(5/4)). - _Vaclav Kotesovec_, Nov 10 2017

%e G.f.: 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 107*x^5 + 218*x^6 + ...

%t nmax = 30; CoefficientList[Series[Product[(1 - x^(5*k))/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)

%Y Cf. Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^k: A035959 (k=1), A160461 (k=2), this sequence (k=3), A278680 (k=4), A277212 (k=5), A182821 (k=6).

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 25 2016