A352307 Expansion of e.g.f. 1/(2 - exp(x) - x^3/6).

1, 1, 3, 14, 83, 621, 5583, 58493, 700507, 9438253, 141291843, 2326680313, 41797029035, 813422096709, 17047913249279, 382815685896293, 9169316015977675, 233352842701661021, 6288004372005738747, 178851946015229702545, 5354894260179239755995

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A006155, A352306, A352308.

Cf. A352299.

Programs

Mathematica

m = 20; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3/6), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^3/6)))

PARI

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

Formula

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