A066053 Stirling transform of A002457.

1, 6, 36, 236, 1686, 13028, 108078, 956348, 8976708, 88962160, 927129786, 10125636716, 115543526476, 1373933166848, 16985192456410, 217851008508220, 2893517713599370, 39732264695056772, 563187218351672330, 8229159647194683140, 123795221970087313340

Offset: 0

Author

Karol A. Penson, Nov 30 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..538

Crossrefs

Cf. A002457, A064856.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0,
      (2*m+1)!/m!^2, m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..23);  # Alois P. Heinz, Jun 23 2023

Mathematica

Table[Sum[StirlingS2[n, k]*(2*k+2)!/(2*k!*(k+1)!), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 01 2018 *)

Formula

a(n) = sum(stirling2(n, k)*(2*k + 2)!/(2*k!*(k + 1)!), k = 0..n), n = 0, 1, ...;

E.g.f.: exp(2*exp(x) - 2)*(BesselI(0, 2*exp(x) - 2) + 4*BesselI(0, 2*exp(x) - 2)*(exp(x) - 1) + 4*(exp(x) - 1)*BesselI(1, 2*exp(x) - 2)).