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Expansion of Product_{k>=0} (1-x^(4*k+1))^(4*k+1).
5

%I #18 Apr 17 2017 05:37:21

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

%T 223,-512,400,-116,362,-1175,1329,-564,609,-2368,3593,-2218,1246,

%U -4402,8600,-7118,3433,-7792,18503,-19778,10702,-13924,37009,-49017,32097,-27141

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

%H Seiichi Manyama, <a href="/A285070/b285070.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (-1)^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 17 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 17 2017 *)

%Y Product_{k>=0} (1-x^(m*k+1))^(m*k+1): A285069 (m=2), A285050 (m=3), this sequence (m=4), A285071 (m=5).

%Y Cf. A285048, A285288.

%K sign

%O 0,6

%A _Seiichi Manyama_, Apr 15 2017