A351905 Expansion of e.g.f. exp(x * (1 - x^3)).

1, 1, 1, 1, -23, -119, -359, -839, 18481, 178417, 902161, 3318481, -69866279, -1011908039, -7204341143, -36194591159, 726745175521, 14326789219681, 131901636673441, 840736509931297, -16060449291985079, -408041402342457239, -4618341644958693959, -35691963052019431079

Offset: 0

Author

Seiichi Manyama, Feb 25 2022

Keywords

• sign

Crossrefs

Cf. A293604, A246607, A351906.

Cf. A190875, A293493.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-x^3))))

PARI

a(n) = n!*sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)/(n-3*k)!);

PARI

a(n) = if(n<4, 1, a(n-1)-4!*binomial(n-1, 3)*a(n-4));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k)/(n-3*k)!.

a(n) = a(n-1) - 4! * binomial(n-1,3) * a(n-4) for n > 3.