A351906 Expansion of e.g.f. exp(x * (1 - x^4)).

1, 1, 1, 1, 1, -119, -719, -2519, -6719, -15119, 1784161, 19902961, 119655361, 518763961, 1815974161, -212497445159, -3472602456959, -29605333299359, -177764320560959, -844590032480159, 97992221659873921, 2116963290135836521, 23379513665735470321

Offset: 0

Author

Seiichi Manyama, Feb 25 2022

Keywords

• sign

Crossrefs

Cf. A293604, A246607, A351905.

Cf. A190877, A293507.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-x^4))))

PARI

a(n) = n!*sum(k=0, n\5, (-1)^k*binomial(n-4*k, k)/(n-4*k)!);

PARI

a(n) = if(n<5, 1, a(n-1)-5!*binomial(n-1, 4)*a(n-5));

Formula

a(n) = n! * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n-4*k,k)/(n-4*k)!.

a(n) = a(n-1) - 5! * binomial(n-1,4) * a(n-5) for n > 4.