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%I #21 Feb 25 2022 07:20:34
%S 1,-1,1,-1,1,-121,721,-2521,6721,-378001,5473441,-39972241,199679041,
%T -7005552841,176899522801,-2186722497961,17454339826561,
%U -459473703430561,16503993702423361,-306140370496394401,3555223271216311681,-80917223353652470681
%N E.g.f.: Product_{m>=0} exp(-x^(4*m+1)).
%H Muniru A Asiru, <a href="/A293566/b293566.txt">Table of n, a(n) for n = 0..50</a>
%F E.g.f.: exp(x/(x^4 - 1)).
%F a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * (4*k+1)! * a(n-4*k-1). - _Ilya Gutkovskiy_, Feb 24 2022
%p seq(factorial(k) * coeftayl(product(exp(-x^(4*m + 1)),m = 0..k), x = 0, k),k = 0..50); # _Muniru A Asiru_, Oct 15 2017
%t CoefficientList[Series[E^(x/(x^4 - 1)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 13 2017 *)
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(x^4-1))))
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(1/prod(m=0, N, exp(x^(4*m+1)))))
%Y E.g.f.: Product_{m>=0} exp(-x^(k*m+1)): A293116 (k=1), A293532 (k=2), A293565 (k=3), this sequence (k=4).
%Y Cf. A293507.
%K sign
%O 0,6
%A _Seiichi Manyama_, Oct 12 2017
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