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A293565
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E.g.f.: Product_{m>=0} exp(-x^(3*m+1)).
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1
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1, -1, 1, -1, -23, 119, -359, -4201, 58801, -359857, -2121839, 74851919, -784376999, -1072414201, 192596540137, -3167640042841, 9241215940321, 860635956717599, -21290802661288799, 157132294452113183, 5980504635868174921, -220612220726623344361
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f.: exp(x/(x^3 - 1)).
a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * (3*k+1)! * a(n-3*k-1). - Ilya Gutkovskiy, Feb 24 2022
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MATHEMATICA
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CoefficientList[Series[E^(x/(x^3 - 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^3-1))))
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(1/prod(m=0, N, exp(x^(3*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), this sequence (k=3), A293566 (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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