A293571 E.g.f.: exp(x/(1 + x + x^2)).

1, 1, -1, -5, 25, 41, -1049, 2899, 54545, -610415, -1363409, 92652011, -651996311, -10663181255, 262674487895, -529402905149, -68312606260319, 1136414207246369, 7701376416944095, -584076369474366245, 6461047290787787321, 173442620419212050761

Offset: 0

Author

Seiichi Manyama, Oct 12 2017

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..446
• Robert Israel, Plot of a(n)/(n! exp(sqrt(n))) for n = 2 .. 2500

Crossrefs

Cf. A111884, A293572, A293573.

Programs

Maple

f:= gfun:-rectoproc({a(n) = (3-2*n)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (5-2*n)*(n-1)*(n-2)*a(n-3)- (n-4)*(n-3)*(n-2)*(n-1)*a(n-4),a(0)=1,a(1)=1,a(2)=-1,a(3)=-5},a(n),remember):
map(f, [$0..30]); # Robert Israel, Jul 27 2020

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1+x+x^2))))

PARI

N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-2)-x^(3*k-1)))))

Formula

E.g.f.: Product_{k>0} exp(x^(3*k-2)) / exp(x^(3*k-1)).

a(n) = (3-2*n)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (5-2*n)*(n-1)*(n-2)*a(n-3) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-4). - Robert Israel, Jul 27 2020