OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..538
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)).
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Nov 30 2001
STATUS
approved