A383437 a(1) = 1; a(n) = 5 + n * Sum_{k=1..n-1} a(k).

1, 7, 29, 153, 955, 6875, 56145, 513325, 5197415, 57749055, 698763565, 9147450305, 128826591795, 1942308614755, 31215674165705, 532747505761365, 9622751822814655, 183398328858349895, 3678155373214684005, 77434849962414400105, 1707438441671237522315

Offset: 1

Author

Seiichi Manyama, Apr 27 2025

Keywords

• nonn

Crossrefs

Cf. A007808, A074143, A082425, A082427, A082428, A082430, A383436.

Cf. A001339.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-5-2*x+(-12*x+5*exp(x))/(1-x)^2))

Formula

E.g.f.: -5 - 2*x + (-12*x + 5*exp(x))/(1-x)^2.

a(n) = -12 * n * n! + 5 * Sum_{k=0..n} (k+1)! * binomial(n,k) for n > 1.

a(n) = (n^2 * a(n-1) - 5)/(n-1) for n > 2.

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