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

0,6

Links

Muniru A Asiru, Table of n, a(n) for n = 0..50

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

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

Mathematica

CoefficientList[Series[E^(x/(x^4 - 1)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 13 2017 *)

Prog

(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)))))

Crossrefs

E.g.f.: Product_{m>=0} exp(-x^(k*m+1)): A293116 (k=1), A293532 (k=2), A293565 (k=3), this sequence (k=4).

Cf. A293507.

Sequence in context: A361636 A354554 A367720 * A293507 A356630 A306452

Adjacent sequences: A293563 A293564 A293565 * A293567 A293568 A293569

Keyword

sign

Author

Seiichi Manyama, Oct 12 2017

Status

approved