OFFSET
0,2
COMMENTS
Stirling transform of A000984.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..539
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Stirling Transform
FORMULA
E.g.f.: exp(2*(exp(x) - 1))*BesselI(0,2*(exp(x) - 1)).
a(n) = Sum_{k=0..n} Stirling2(n,k)*binomial(2*k,k).
MAPLE
b:= proc(n, m) option remember;
`if`(n=0, binomial(2*m, 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 = 22; CoefficientList[Series[Sum[Binomial[2 k, k] x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 22; CoefficientList[Series[Exp[2 (Exp[x] - 1)] BesselI[0, 2 (Exp[x] - 1)], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] Binomial[2 k, k], {k, 0, n}], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 31 2018
STATUS
approved