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A372117
a(n) = Product_{k=0..n} binomial(n+k, k)^k.
0
1, 2, 108, 3200000, 1158107343750000, 119025168578031262646195453952, 82864944710388642300699757862681018776776867840000, 9481019710293786574190900386319772308050021208649248212215823364196925440000000
OFFSET
0,2
FORMULA
a(n) = Product_{k=0..n} binomial(n + k, n)^k.
a(n) = A372116(n) / (A255269(n) * A067055(n)).
a(n) ~ 2^(2*n^3/3 + 3*n^2/4 + n/6 + 1/24) * exp(n^3/12 + n^2/4 - n/24 + zeta(3)/(8*Pi^2) - 1/24) / (sqrt(A) * Pi^(n^2/4 + n/4) * n^(n^2/4 + n/4 + 1/24)), where A is the Glaisher-Kinkelin constant A074962.
MATHEMATICA
Table[Product[Binomial[n+k, k]^k, {k, 0, n}], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 19 2024
STATUS
approved