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A329928
a(n) = (Pi/2)*(2*n+1)!*binomial(2*n+1, (2*n+1)/2).
0
2, 32, 2048, 294912, 75497472, 30198988800, 17394617548800, 13637380158259200, 13964677282057420800, 18098221757546417356800, 28957154812074267770880000, 56061051716175782404423680000, 129164663154069002659792158720000, 349261249168602583192077997178880000
OFFSET
0,1
FORMULA
a(n) = 2^(4*n + 1)*Gamma(n + 1)^2.
a(n) = a(n-1)*(4*n)^2 for n > 0.
MAPLE
a := proc(n) option remember; if n = 0 then 2 else 16*a(n-1)*n^2 fi end:
seq(a(n), n = 0..13);
PROG
(PARI) \p100; binom(n, k)=gamma(n+1)/(gamma(k+1)*gamma(n-k+1));
for(n=0, 14, print1(round((Pi/2)*(2*n+1)!*binom(2*n+1, (2*n+1)/2)), ", ")) \\ Hugo Pfoertner, Dec 05 2019
CROSSREFS
Sequence in context: A087084 A193269 A088386 * A093584 A117259 A234365
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 05 2019
STATUS
approved