A346417 E.g.f.: exp(exp(2*(exp(x) - 1)) - 1).

1, 2, 10, 66, 538, 5186, 57402, 714594, 9853978, 148774914, 2436823034, 42979319202, 811254807770, 16302732719682, 347248840767162, 7809649226242530, 184831773033020826, 4589793199157616770, 119272846472231229818, 3235960069037751550498, 91466308730323104617050

Offset: 0

Author

Ilya Gutkovskiy, Jul 16 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000258, A000898, A001861, A055882, A126390, A136658.

Programs

Maple

b:= proc(n, t, m) option remember; `if`(n=0, `if`(t=1, 1,
      b(m, 1, 0)*2^m) , m*b(n-1, t, m)+b(n-1, t, m+1))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 06 2021

Mathematica

nmax = 20; CoefficientList[Series[Exp[Exp[2 (Exp[x] - 1)] - 1], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] 2^k BellB[k], {k, 0, n}], {n, 0, 20}]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] BellB[k, 2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

PARI

my(x='x+O('x^25)); Vec(serlaplace(exp(exp(2*(exp(x) - 1)) - 1))) \\ Michel Marcus, Jul 19 2021

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k) * 2^k * Bell(k).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A001861(k) * a(n-k).