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A293566
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E.g.f.: Product_{m>=0} exp(-x^(4*m+1)).
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2
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1, -1, 1, -1, 1, -121, 721, -2521, 6721, -378001, 5473441, -39972241, 199679041, -7005552841, 176899522801, -2186722497961, 17454339826561, -459473703430561, 16503993702423361, -306140370496394401, 3555223271216311681, -80917223353652470681
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OFFSET
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0,6
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LINKS
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FORMULA
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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
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MAPLE
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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
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CoefficientList[Series[E^(x/(x^4 - 1)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 13 2017 *)
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PROG
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(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)))))
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CROSSREFS
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E.g.f.: Product_{m>=0} exp(-x^(k*m+1)): A293116 (k=1), A293532 (k=2), A293565 (k=3), this sequence (k=4).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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