A345178 a(0) = 0, a(1) = 1; a(n+2) = Sum_{k=0..n} Stirling2(n,k) * a(k).

0, 1, 0, 1, 1, 2, 8, 38, 194, 1138, 8154, 71544, 739406, 8674238, 113451160, 1648133190, 26631054962, 478633871152, 9531297220728, 208851860234540, 4997665703050398, 129765874491438094, 3639593254921626678, 109942671192206473592, 3569449102675488493032, 124319448405579907085938

Offset: 0

Author

Ilya Gutkovskiy, Jun 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..355

Crossrefs

Cf. A000995, A003659, A007469, A345177.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0,
      a(m), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> `if`(n<2, n, b(n-2, 0)):
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 13 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]
nmax = 25; A[] = 0; Do[A[x] = x + Normal[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], x], x] + O[x]^(nmax + 1)], nmax]; CoefficientList[A[x], x] Range[0, nmax]!