A366305 a(n) = Product_{k=1..n} (k^n + (k-1)^n).
1, 5, 315, 555713, 47705305725, 305469864195354625, 207095306530955763265880535, 20017329298655447986400838721630926977, 357361761140807273279996172600335233468472149678425, 1481824279740988988264353294673429995981921700740921435758587890625
Offset: 1
Keywords
Programs
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Mathematica
Table[Product[k^n + (k-1)^n, {k, 1, n}], {n, 1, 10}]
Formula
a(n) = (n!)^n * Product_{k=1..n} (1 + (1 - 1/k)^n).
a(n) ~ n!^n * d^n, where d = exp(Integral_{x=0..1} log(1 + exp(-1/x)) dx) = 1.14183186235785012136459060138978468902610644657603999829892450823456733...
a(n) ~ (2*Pi)^(n/2) * d^n * n^(n*(2*n+1)/2) / exp(n^2 - 1/12).