A345177 a(0) = 1, a(1) = 0; a(n+2) = Sum_{k=0..n} Stirling2(n,k) * a(k).

1, 0, 1, 0, 1, 3, 8, 28, 149, 1029, 8039, 69375, 675541, 7584630, 98484836, 1457695370, 24117255106, 439505090491, 8756668806615, 190293641816660, 4508138040317573, 116298682305458460, 3258081214212853975, 98709283556190931672, 3219222306795403565116, 112538217720491999726102

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. A000994, A003659, A007469, A345178.

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, 1-n, b(n-2, 0)):
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 13 2021

Mathematica

a[0] = 1; a[1] = 0; 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] = 1 + 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]!