|
|
A365266
|
|
a(n) = Product_{k=1..n} Gamma(6*k).
|
|
0
|
|
|
1, 120, 4790016000, 1703748471578689536000000, 44045334006101976766560297729172439040000000000, 389438360216723307909581902233109465138002465491175688781168640000000000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = A^(35/6) * exp(-35/72) * Gamma(1/3)^(5/3) * 2^(-125/72 + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * Pi^(-25/12 - 5*n/2) * BarnesG(1 + n) * BarnesG(7/6 + n) * BarnesG(4/3 + n) * BarnesG(3/2 + n) * BarnesG(5/3 + n) * BarnesG(11/6 + n), where A = A074962 is the Glaisher-Kinkelin constant.
a(n) ~ A^(-1/6) * Gamma(1/3)^(5/3) * 2^(-35/72 + 3*n + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * exp(1/72 - 5*n/2 - 9*n^2/2) * n^(19/72 + 5*n/2 + 3*n^2) * Pi^(-5/6 + n/2), where A = A074962 is the Glaisher-Kinkelin constant.
|
|
MATHEMATICA
|
Table[Product[Gamma[6*k], {k, 1, n}], {n, 0, 10}]
Table[Product[(6*k-1)!, {k, 1, n}], {n, 0, 10}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|