A383436 a(1) = 1; a(n) = 2 + n * Sum_{k=1..n-1} a(k).

1, 4, 17, 90, 562, 4046, 33042, 302098, 3058742, 33986022, 411230866, 5383385882, 75816017838, 1143072268942, 18370804322282, 313528393766946, 5663106612415462, 107932149554271158, 2164639221616216002, 45571352034025600042, 1004848312350264480926, 23159361103691809941342

Offset: 1

Author

Seiichi Manyama, Apr 27 2025

Keywords

• nonn

Crossrefs

Cf. A007808, A074143, A082425, A082427, A082428, A082430, A383437.

Cf. A001339.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-2-x/2+(-9*x/2+2*exp(x))/(1-x)^2))

Formula

E.g.f.: -2 - x/2 + (-9*x/2 + 2*exp(x))/(1-x)^2.

a(n) = -9*n/2 * n! + 2 * Sum_{k=0..n} (k+1)! * binomial(n,k) for n > 1.

a(n) = (n^2 * a(n-1) - 2)/(n-1) for n > 2.

a(n) = (n+2) * a(n-1) - (n-1) * a(n-2) for n > 3.