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%I #19 Nov 28 2016 05:54:37
%S 1,25,350,3575,29575,209381,1312075,7443825,38854075,188836375,
%T 862496902,3729343275,15356254650,60511763600,229125615600,
%U 836555203223,2953900713000,10113407774450,33649438734125,109017926343725,344525085375315,1063718962906450
%N Expansion of Product_{n>=1} (1 - x^(5*n))^24/(1 - x^n)^25 in powers of x.
%H Seiichi Manyama, <a href="/A278557/b278557.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(5*n))^24/(1 - x^n)^25.
%F A278559(n) = 5^2*63*A160460(n) + 5^5*52*A278555(n-1) + 5^7*63*A278556(n-2) + 5^10*6*a(n-3) + 5^12*A278558(n-4) for n >= 4.
%F a(n) ~ sqrt(101/15) * exp(Pi*sqrt(202*n/15)) / (976562500*n). - _Vaclav Kotesovec_, Nov 28 2016
%t nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^24/(1 - x^k)^25, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 28 2016 *)
%Y Cf. A160460, A278555, A278556, A278558, A278559.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 23 2016