A028248 Expansion of exp(exp(exp(x) - 1 - x) - 1).

1, 0, 1, 1, 7, 21, 126, 638, 4264, 28983, 226018, 1872300, 16940661, 163461455, 1688378030, 18501971647, 214749109038, 2628228896227, 33832314246857, 456730760934125, 6451399211318995, 95135434800384144, 1461771954435844296, 23360315241127222572

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

For p prime, a(p) == 1 (mod p) and a(p+1) == 1 (mod p). - Mélika Tebni, Mar 22 2022

Examples

			From _Mélika Tebni_, Mar 22 2022: (Start)
a(11) = Sum_{k=0..5} (-1)^k*Bell(k)*A137375(11, k) = 1*(0) - 1*(-1) + 2*(1012) - 5*(-22935) + 15*(56980) - 52*(-17325) = 1872300. (End)
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..495

Crossrefs

Cf. A000110, A137375, A352607.

Programs

Maple

h:= proc(n, m) option remember;
     `if`(n=0, 1, h(n-1, m+1)+m*h(n-1, m))
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1)*h(j, -1), j=1..n))
    end:
seq(a(n), n=0..23);  # Alois P. Heinz, Apr 14 2023

Mathematica

A352607[n_, k_] := BellB[k]*Sum[(-1)^(k + j)*Binomial[n, n - k + j]* StirlingS2[n - k + j, j], {j, 0, k}]; a[n_] := Sum[A352607[n, k], {k, 0, Floor[n/2]}]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Oct 21 2023 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(exp(exp(x) - 1 - x) - 1))) \\ Michel Marcus, Mar 22 2022

Formula

Row sums of A352607. - Mélika Tebni, Mar 22 2022