A293566 E.g.f.: Product_{m>=0} exp(-x^(4*m+1)).
1, -1, 1, -1, 1, -121, 721, -2521, 6721, -378001, 5473441, -39972241, 199679041, -7005552841, 176899522801, -2186722497961, 17454339826561, -459473703430561, 16503993702423361, -306140370496394401, 3555223271216311681, -80917223353652470681
Offset: 0
Keywords
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..50
Crossrefs
Programs
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Maple
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
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Mathematica
CoefficientList[Series[E^(x/(x^4 - 1)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 13 2017 *) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(x^4-1)))) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(1/prod(m=0, N, exp(x^(4*m+1)))))
Formula
E.g.f.: exp(x/(x^4 - 1)).
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