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A272869
a(n) = n^n*GegenbauerC(n,-n,-1/n)/(n+1).
0
1, 4, 29, 464, 6922, 202432, 4630173, 198818048, 6154090622, 349818973184, 13677614598386, 969203418615808, 45826572523307188, 3892801508457267200, 216012496119594222173, 21401823901203257425920, 1363592394593251194183414, 154410199210675432076345344
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
Sequence in context: A277357 A173715 A230326 * A166168 A126559 A213795
KEYWORD
nonn
AUTHOR
Peter Luschny, May 08 2016
STATUS
approved