OFFSET
0,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..60
FORMULA
a(n) = Product_{k=0..(n-1)} 3(k+1)*A000108(k+1)/(k+3).
a(n) = Product_{k=0..(n-1)} A000245(k+1).
a(n) = (A^(3/2) 2^(n(n+1))*2^(23/24)*3^n*Pi^(-1/4-n/2)*G(n+3/2)*Gamma(n+1)) /(e^(1/8)*G(n+4)), where G is Barnes G-function, and A is the Glaisher-Kinkelin constant (A074962) (reported by Wolfram Alpha).
a(n) ~ A^(3/2) * 2^(n^2+n+5/24) * 3^n * exp(3*n/2-1/8) / (n^(3*n/2+31/8) * Pi^(n/2+1)), where A = 1.2824271291... is the Glaisher-Kinkelin constant (see A074962). - Vaclav Kotesovec, Nov 14 2014
MATHEMATICA
Table[Product[3*(2*k+2)!/((k+3)!*k!), {k, 0, n-1}], {n, 0, 10}] (* Vaclav Kotesovec, Nov 14 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 15 2011
STATUS
approved