OFFSET
0,3
COMMENTS
Lah transform of the Catalan numbers (A000108).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..435
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: exp(2*x/(1 - x))*(BesselI(0,2*x/(1 - x)) - BesselI(1,2*x/(1 - x))).
a(n) ~ exp(4*sqrt(n) - n - 2) * n^(n-1) / (2*sqrt(2*Pi)). - Vaclav Kotesovec, Jun 07 2019
MATHEMATICA
Table[Sum[Binomial[n - 1, k - 1] Binomial[2 k, k] n!/(k + 1)!, {k, 0, n}], {n, 0, 21}]
nmax = 21; CoefficientList[Series[Exp[2 x/(1 - x)] (BesselI[0, 2 x/(1 - x)] - BesselI[1, 2 x/(1 - x)]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[n! HypergeometricPFQ[{3/2, 1 - n}, {2, 3}, -4], {n, 21}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 25 2018
STATUS
approved