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Expansion of Product_{k>=0} (1 + x^(4*k+1))^(4*k+1).
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%I #14 Apr 16 2017 10:27:29

%S 1,1,0,0,0,5,5,0,0,9,19,10,0,13,58,55,10,17,118,191,95,26,223,512,400,

%T 116,362,1175,1329,564,609,2368,3593,2218,1246,4402,8600,7118,3433,

%U 7792,18503,19778,10702,13924,37009,49017,32097,27141,69629,111251,88972

%N Expansion of Product_{k>=0} (1 + x^(4*k+1))^(4*k+1).

%H Seiichi Manyama, <a href="/A285288/b285288.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (-1)^n * A285070(n).

%F a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - _Vaclav Kotesovec_, Apr 16 2017

%t nmax = 50; CoefficientList[Series[Product[(1 + x^(4*k-3))^(4*k-3), {k,1,nmax}], {x,0,nmax}], x] (* _Vaclav Kotesovec_, Apr 16 2017 *)

%Y Product_{k>=0} (1 + x^(m*k+1))^(m*k+1): A262736 (m=2), A262949 (m=3), this sequence (m=4).

%Y Cf. A285070, A285287.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Apr 16 2017