OFFSET
0,3
COMMENTS
Stirling transform of A006882.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..517
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Stirling Transform
FORMULA
E.g.f.: 1 + exp((exp(x) - 1)^2/2)*(exp(x) - 1)*(1 + sqrt(Pi/2)*erf((exp(x) - 1)/sqrt(2))).
a(n) = Sum_{k=0..n} Stirling2(n,k)*k!!.
MAPLE
b:= proc(n, m) option remember;
`if`(n=0, doublefactorial(m), 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, Aug 04 2021
MATHEMATICA
nmax = 23; CoefficientList[Series[Sum[k!! x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 23; CoefficientList[Series[1 + Exp[(E^x - 1)^2/2] (Exp[x] - 1) (1 + Sqrt[Pi/2] Erf[(Exp[x] - 1)/Sqrt[2]]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] k!!, {k, 0, n}], {n, 0, 23}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 31 2018
STATUS
approved