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

0,5

Links

Table of n, a(n) for n=0..23.

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.

Prog

(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));

Crossrefs

Cf. A293604, A246607, A351906.

Cf. A190875, A293493.

Sequence in context: A253679 A303411 A069756 * A337751 A362339 A358063

Adjacent sequences: A351902 A351903 A351904 * A351906 A351907 A351908

Keyword

sign

Author

Seiichi Manyama, Feb 25 2022

Status

approved