OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..449
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).
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}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(exp(2*(exp(x) - 1)) - 1))) \\ Michel Marcus, Jul 19 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 16 2021
STATUS
approved