|
%I #9 Jan 24 2017 09:50:00
%S 1,0,0,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,2,0,1,1,0,2,0,1,1,0,3,0,1,
%T 2,0,3,0,1,3,0,4,1,1,4,0,4,1,1,5,0,5,2,1,7,0,5,3,1,8,0,6,5,1,10,1,6,6,
%U 1,12,1,7,9,1,14,2,7,11,1,16,3,8,15,1
%N Expansion of Product_{k>=1} (1 + x^(5*k-2)).
%H Vaclav Kotesovec, <a href="/A281271/b281271.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ exp(sqrt(n/15)*Pi) / (2^(8/5)*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 - 2)), {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] == 3, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly
%Y Cf. A219607, A281243, A281272, A280454.
%K nonn
%O 0,22
%A _Vaclav Kotesovec_, Jan 18 2017
|
