A352299 Expansion of e.g.f. 1/(2 - exp(x) - x^3).

1, 1, 3, 19, 123, 1021, 10683, 127093, 1725867, 26535613, 452307243, 8475606613, 173390108235, 3842119808749, 91675559886459, 2343875745873493, 63920729617231275, 1852126733351677021, 56823327291638414667, 1840195730889731550805

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A006155, A346269, A352300.

Cf. A352303, A352307.

Programs

Mathematica

m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-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.