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.
%I A255344 #16 Aug 05 2025 19:29:02
%S A255344 1,4294967296
%N A255344 Product_{k=1..n} k^(k^5).
%C A255344 The next terms: a(3) has 126 digits, a(4) has 743 digits, a(5) has 2927 digits.
%C A255344 In general, product_{k=1..n} k^(k^m) ~ A(m) * n^(B(m+1)/(m+1) + sum_{j=1..n} j^m) * exp(-n^(m+1)/(m+1)^2 + sum_{j=1..m-1} (1/(j+1) * B(j+1) * binomial(m,j) * n^(m-j) * sum_{i=0..j-1} 1/(m-i) )), where A(m) is the generalized Glaisher-Kinkelin constant (see A074962, A243262, A243263, A243264, A243265), and B(n) is the Bernoulli number A027641(n) / A027642(n).
%D A255344 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.
%H A255344 Vaclav Kotesovec, <a href="/A255344/b255344.txt">Table of n, a(n) for n = 1..4</a>
%F A255344 a(n) ~ A243265 * n^(n^2*(n+1)^2*(2*n^2+2*n-1)/12 + 1/252) / exp(47*n^2/720 - n^4/12 + n^6/36).
%t A255344 Table[Product[k^(k^5), {k, 1, n}], {n, 1, 5}]
%t A255344 FoldList[Times,Table[k^k^5,{k,5}]] (* _Harvey P. Dale_, Aug 05 2025 *)
%o A255344 (PARI) a(n)=prod(k=2,n,k^k^5) \\ _Charles R Greathouse IV_, Sep 08 2015
%Y A255344 Cf. A002109, A051675, A255321, A255323, A243265.
%K A255344 nonn
%O A255344 1,2
%A A255344 _Vaclav Kotesovec_, Feb 21 2015