A352303 Expansion of e.g.f. 1/(exp(x) - x^3).

1, -1, 1, 5, -47, 239, -239, -11761, 170689, -1237825, -2360159, 238756319, -4146035519, 32586126143, 359988680689, -18567245926321, 351652342984321, -2283764958280321, -89760640709677247, 3866819337993369023, -74731210747948586879, 167887841949213912959

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• sign

Crossrefs

Cf. A089148, A352302, A352304.

Cf. A352299.

Programs

Mathematica

m = 21; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^3), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

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

PARI

b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 3);

Formula

a(n) = n * (n-1) * (n-2) * a(n-3) - Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.

a(n) = n! * Sum_{k=0..floor(n/3)} (-k-1)^(n-3*k)/(n-3*k)!. - Seiichi Manyama, Aug 21 2024