OFFSET
1,2
FORMULA
a(n) = (-n)^n*Catalan(n)*Hypergeom([-n,-n], [-n+1/2], (1+1/n)/2).
a(n) ~ (exp(1) + (-1)^n * exp(-1)) * 2^n * n^(n - 3/2) / sqrt(2*Pi). - Vaclav Kotesovec, Jul 09 2018
MAPLE
a := n -> simplify(n^n*GegenbauerC(n, -n, -1/n)/(n+1)):
seq(a(n), n=1..18);
MATHEMATICA
Table[n^n GegenbauerC[n, -n, -1/n]/(n + 1), {n, 18}] (* Michael De Vlieger, May 08 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, May 08 2016
STATUS
approved