cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A366305 a(n) = Product_{k=1..n} (k^n + (k-1)^n).

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%I A366305 #7 Oct 07 2023 08:48:40
%S A366305 1,5,315,555713,47705305725,305469864195354625,
%T A366305 207095306530955763265880535,20017329298655447986400838721630926977,
%U A366305 357361761140807273279996172600335233468472149678425,1481824279740988988264353294673429995981921700740921435758587890625
%N A366305 a(n) = Product_{k=1..n} (k^n + (k-1)^n).
%F A366305 a(n) = (n!)^n * Product_{k=1..n} (1 + (1 - 1/k)^n).
%F A366305 a(n) ~ n!^n * d^n, where d = exp(Integral_{x=0..1} log(1 + exp(-1/x)) dx) = 1.14183186235785012136459060138978468902610644657603999829892450823456733...
%F A366305 a(n) ~ (2*Pi)^(n/2) * d^n * n^(n*(2*n+1)/2) / exp(n^2 - 1/12).
%t A366305 Table[Product[k^n + (k-1)^n, {k, 1, n}], {n, 1, 10}]
%Y A366305 Cf. A036740, A323575, A323588, A323589, A366306.
%K A366305 nonn
%O A366305 1,2
%A A366305 _Vaclav Kotesovec_, Oct 06 2023