A372116 a(n) = Product_{k=0..n} (n+k)!^k.
1, 2, 3456, 128994508800000, 21048441369734473363614597120000000000, 13080442484467245346116306952031286205761554346416540536012800000000000000000000
Offset: 0
Keywords
Programs
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Mathematica
Table[Product[(n + k)!^k, {k, 0, n}], {n, 0, 8}]
Formula
a(n) ~ 2^(2*n^3/3 + 5*n^2/4 + 2*n/3 + 1/24) * Pi^(n*(n+1)/4) * n^(5*n^3/6 + 5*n^2/4 + 5*n/12) / exp(31*n^3/36 + 7*n^2/8 - 1/24).
For n>=1, a(n) = a(n-1) * A368132(n) * (2*n-1)!^n.
Comments