A368762 a(n) = n! * (1 + Sum_{k=0..n} binomial(k+1,2) / k!).

1, 2, 7, 27, 118, 605, 3651, 25585, 204716, 1842489, 18424945, 202674461, 2432093610, 31617217021, 442641038399, 6639615576105, 106233849217816, 1805975436703025, 32507557860654621, 617643599352437989, 12352871987048759990, 259410311728023960021

Offset: 0

Author

Seiichi Manyama, Jan 04 2024

Keywords

• nonn

Crossrefs

Cf. A033540, A368763, A368764.

Cf. A103519, A368766.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x*sum(k=0, 1, binomial(1, k)*x^k/(k+1)!)*exp(x))/(1-x)))

Formula

a(0) = 1; a(n) = n*a(n-1) + binomial(n+1,2).

a(n) = n! + A103519(n).

E.g.f.: (1 + x * (1+x/2) * exp(x)) / (1-x).