OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..61
FORMULA
a(n) ~ exp(1/24) * 2^(2/3 + 5*n + 8*n^2) / (sqrt(A) * n^(1/24) * 3^(9*n^2/2 + 3*n + 5/12)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 26 2023
EXAMPLE
a(0) = 1: ().
/\
a(1) = 2: (/\/\), (/ \).
MAPLE
a:= n-> mul(mul((i+j+2*n)/(i+j), j=i..n), i=1..n):
seq(a(n), n=0..14);
MATHEMATICA
Join[{1}, Table[2^(3/2)*n*Gamma[4*n] * BarnesG[n+1] * Sqrt[Gamma[2*n] * BarnesG[4*n]] / BarnesG[3*n + 2], {n, 1, 12}]] (* Vaclav Kotesovec, Aug 26 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 24 2023
STATUS
approved