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 A263430 #17 Feb 16 2025 08:33:27
%S A263430 1,1,5,225,131625,1309010625,273380323978125,1427352844030287890625,
%T A263430 216119240915841469025244140625,
%U A263430 1079864992142473709995957417730712890625,199639840782299404795675492100337942688751220703125
%N A263430 a(n) = Product_{k=0..n} (4*k+1)^(n-k).
%H A263430 G. C. Greubel, <a href="/A263430/b263430.txt">Table of n, a(n) for n = 0..36</a>
%H A263430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalansConstant.html">Catalan's Constant</a>
%H A263430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>
%F A263430 a(n) ~ A^(1/8) * 2^(n^2 + 3*n/2 + 1/8) * Pi^(n/2 + 1/8) * n^(n^2/2 + n/4 - 5/96) / (Gamma(1/4)^(n + 1/4) * exp(3*n^2/4 + n/4 + 1/96 - C/(4*Pi))), where A = A074962 is the Glaisher-Kinkelin constant and C = A006752 = is Catalan's constant.
%t A263430 Table[Product[(4*k+1)^(n-k),{k,0,n}],{n,0,10}]
%o A263430 (PARI) for(n=0,10, print1(prod(k=0,n, (4*k+1)^(n-k)), ", ")) \\ _G. C. Greubel_, Aug 25 2018
%o A263430 (Magma) [(&*[(4*k+1)^(n-k): k in [0..n]]): n in [0..10]]; // _G. C. Greubel_, Aug 25 2018
%Y A263430 Cf. A000178, A057863, A263416.
%K A263430 nonn
%O A263430 0,3
%A A263430 _Vaclav Kotesovec_, Oct 18 2015