A352306 Expansion of e.g.f. 1/(2 - exp(x) - x^2/2).

1, 1, 4, 19, 129, 1071, 10743, 125455, 1675439, 25167073, 420070323, 7712503173, 154475622513, 3351859639363, 78324320723561, 1960968388497523, 52368881358012435, 1485952518531483045, 44643697199669589447, 1415782273405809697009

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A006155, A352307, A352308.

Cf. A346269, A352309.

Programs

Mathematica

m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^2/2), {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^2/2)))

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, 2);

Formula

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