OFFSET
0,2
FORMULA
a(n) = Product_{k=0..n} ((k+1)*(4k+1)*(4k+3)*floor((2k+3)/2))^(n-k).
a(n) ~ sqrt(Gamma(1/4)) * 2^(2*n^2 + 7*n/2 + 9/8) * n^(n*(2*n+3) + 47/48) * Pi^(n + 3/4) / (A^(7/4) * exp(3*n*(n+1) - 7/48)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019
MATHEMATICA
Table[Product[((k+1)*(4*k+1)*(4*k+3)*Floor[(2*k+3)/2])^(n-k), {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Feb 24 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 30 2010
EXTENSIONS
a(5) and following corrected by Georg Fischer, Jan 18 2024
STATUS
approved