A293532 Expansion of e.g.f. exp(x/(x^2 - 1)).

1, -1, 1, -7, 25, -181, 1201, -10291, 97777, -1013545, 12202561, -151573951, 2173233481, -31758579997, 524057015665, -8838296029291, 164416415570401, -3145357419120721, 65057767274601217, -1391243470549894135, 31671795881695430521, -747996624368605997701

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..444

Formula

E.g.f.: Product_{k>=1} 1/(1 + x^k)^(phi(k)/k), where phi() is the Euler totient function (A000010). - Ilya Gutkovskiy, May 25 2019

D-finite with recurrence: n*(n + 1)*(n + 2)*(n + 3)*a(n) + (n + 3)*(n + 2)*a(n + 1) - 2*(n + 3)*(n + 2)*a(n + 2) + a(n + 3) + a(n + 4) = 0. - Robert Israel, Feb 22 2026

Maple

f:= gfun:-rectoproc({n*(n + 1)*(n + 2)*(n + 3)*a(n) + (n + 3)*(n + 2)*a(n + 1) - 2*(n + 3)*(n + 2)*a(n + 2) + a(n + 3) + a(n + 4), a(0)=1, a(1)=-1, a(2)=1, a(3)=-7}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Feb 22 2026

Mathematica

CoefficientList[Series[E^(x/(x^2 - 1)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 12 2017 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x/(x^2-1))))

Crossrefs

Column k=2 of A293530.

Cf. A088009.

Sequence in context: A366941 A191237 A088009 * A356628 A208823 A197913

Adjacent sequences: A293529 A293530 A293531 * A293533 A293534 A293535

Keyword

sign

Author

Seiichi Manyama, Oct 11 2017

Status

approved