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%I #18 Apr 30 2017 07:38:45
%S 1,5,20,65,190,501,1240,2890,6440,13775,28502,57205,111880,213670,
%T 399620,733128,1321850,2345340,4100700,7072520,12045005,20272465,
%U 33746060,55595635,90706390,146638756,235016940,373580735,589238640,922537655,1434232510,2214817165
%N Expansion of (Product_{k>0} (1 - x^(5*k)) / (1 - x^k))^5 in powers of x.
%C In general, if m > 1 and g.f. = Product_{k>=1} ((1 - x^(m*k)) / (1 - x^k))^m, then a(n, m) ~ exp(Pi*sqrt(2*(m-1)*n/3)) * (m-1)^(1/4) / (2^(5/4) * 3^(1/4) * m^(m/2) * n^(3/4)). - _Vaclav Kotesovec_, Apr 30 2017
%H Seiichi Manyama, <a href="/A285928/b285928.txt">Table of n, a(n) for n = 0..10000</a>
%F a(0) = 1, a(n) = (5/n)*Sum_{k=1..n} A116073(k)*a(n-k) for n > 0.
%F a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * 5^(5/2) * n^(3/4)). - _Vaclav Kotesovec_, Apr 30 2017
%t nmax = 40; CoefficientList[Series[Product[((1 - x^(5*k)) / (1 - x^k))^5, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 30 2017 *)
%Y (Product_{k>0} (1 - x^(m*k)) / (1 - x^k))^m: A022567 (m=2), A285927 (m=3), A093160 (m=4), this sequence (m=5).
%Y Cf. A035959, A285932.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 28 2017
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