A351930 Expansion of e.g.f. exp(x - x^4/24).

1, 1, 1, 1, 0, -4, -14, -34, -34, 190, 1366, 5446, 11056, -30744, -421420, -2403764, -7434244, 9782396, 296347996, 2257819420, 9461601856, -1690329584, -395833164264, -3872875071064, -20629371958040, -17208144880024, 893208132927176, 10962683317693576

Offset: 0

Author

Seiichi Manyama, Feb 26 2022

Keywords

• sign

Crossrefs

Cf. A351929, A351931.

Cf. A351905, A351932.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
     `if`(n<4, 0, -a(n-4)*binomial(n-1, 3))+a(n-1))
    end:
seq(a(n), n=0..27);  # Alois P. Heinz, Feb 26 2022

PARI

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

PARI

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

PARI

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (-1/24)^k * binomial(n-3*k,k)/(n-3*k)!.

D-finite with recurrence a(n) = a(n-1) - binomial(n-1,3) * a(n-4) for n > 3.