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Expansion of Product_{k>=1} (1 + x^(5*k-3)).
8

%I #9 Jan 24 2017 09:49:51

%S 1,0,1,0,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,2,0,1,1,0,2,0,1,1,0,3,0,2,1,0,

%T 3,0,3,1,1,4,0,4,1,1,4,0,5,1,2,5,0,7,1,3,5,0,8,1,5,6,1,10,1,6,6,1,12,

%U 1,9,7,2,14,1,11,7,3,16,1,15,8,5,19,1,18

%N Expansion of Product_{k>=1} (1 + x^(5*k-3)).

%H Vaclav Kotesovec, <a href="/A281272/b281272.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(sqrt(n/15)*Pi) / (2^(7/5)*15^(1/4)*n^(3/4)) * (1 - (3*sqrt(15)/(8*Pi) + 11*Pi/(240*sqrt(15))) / sqrt(n)). - _Vaclav Kotesovec_, Jan 18 2017, extended Jan 24 2017

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(5*k - 3)), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 5] == 2, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

%Y Cf. A219607, A281243, A281271, A280454.

%K nonn

%O 0,20

%A _Vaclav Kotesovec_, Jan 18 2017