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.

A367492 a(n) = Product_{k=0..n} (k+1)!^k.

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%I A367492 #10 Feb 19 2024 02:04:27
%S A367492 1,2,72,995328,206391214080000,39934999921327865856000000000,
%T A367492 654541076770994951831125144608178176000000000000000,
%U A367492 113391518341540395635327816456127297986876881699306137641287680000000000000000000000
%N A367492 a(n) = Product_{k=0..n} (k+1)!^k.
%H A367492 G. C. Greubel, <a href="/A367492/b367492.txt">Table of n, a(n) for n = 0..15</a>
%F A367492 a(n) ~ A^(3/2) * n^(n^3/3 + 5*n^2/4 + 11*n/12 - 3/8) * (2*Pi)^(n^2/4 + n/4 - 1/2) / exp(4*n^3/9 + 7*n^2/8 - n + zeta(3)/(8*Pi^2) - 25/24), where A is the Glaisher-Kinkelin constant A074962.
%F A367492 a(n) = (n+1)^n * abs(A203421(n)) * A255269(n).
%t A367492 Table[Product[(k+1)!^k, {k, 0, n}], {n, 0, 10}]
%o A367492 (Magma) [(&*[Factorial(k+1)^k: k in [0..n]]): n in [0..15]]; // _G. C. Greubel_, Feb 18 2024
%o A367492 (SageMath) [product(factorial(k+1)^k for k in range(n+1)) for n in range(16)] # _G. C. Greubel_, Feb 18 2024
%Y A367492 Cf. A203421, A255269.
%K A367492 nonn
%O A367492 0,2
%A A367492 _Vaclav Kotesovec_, Nov 20 2023