OFFSET
0,2
FORMULA
a(n)=(1/2^n)*{prod(k=1, n, (2*k)!/k!)}^2.
a(n) ~ A * 2^(2*n^2 + 2*n + 5/12) * n^(n^2 + n + 1/12) / exp(3*n^2/2 + n + 1/12), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, May 01 2015
MAPLE
seq(mul(mul(k+j, j=1..n), k=0..n), n=0..7); # Zerinvary Lajos, Jun 01 2007
MATHEMATICA
Table[1/2^n*(Product[(2*k)!/k!, {k, 1, n}])^2, {n, 0, 10}] (* Vaclav Kotesovec, May 01 2015 *)
Table[2^(2*n^2 + n - 1/12) * Glaisher^3 * BarnesG[n+3/2]^2 / (E^(1/4) * Pi^(n+1/2)), {n, 0, 10}] (* Vaclav Kotesovec, May 01 2015 *)
PROG
(PARI) a(n)=(1/2^n)*prod(k=1, n, (2*k)!/k!)^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Mar 19 2005
STATUS
approved