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.

A341782 a(n) = sqrt( Product_{j=1..n} Product_{k=1..n-1} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin(2*k*Pi/n)^2) ).

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%I A341782 #19 Mar 18 2023 05:38:39
%S A341782 1,1,2,112,2312,1270016,292820000,1522266730496,3772667519238272,
%T A341782 193509323594243571712,5041011532336819845120512,
%U A341782 2610531939025273190037188509696
%N A341782 a(n) = sqrt( Product_{j=1..n} Product_{k=1..n-1} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin(2*k*Pi/n)^2) ).
%H A341782 Seiichi Manyama, <a href="/A341782/b341782.txt">Table of n, a(n) for n = 0..62</a>
%F A341782 If n is odd, a(n) = A341535(n)/2.
%F A341782 If n is odd, a(n) = A341478(n).
%F A341782 a(n) ~ exp(2*G*n^2/Pi) / (2^(3/4) * (1 + (1 + (-1)^n)/sqrt(2))), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Mar 18 2023
%t A341782 Table[Sqrt[Product[Product[(4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[2*k*Pi/n]^2), {j, 1, n}], {k, 1, n - 1}]], {n, 0, 15}] // Round (* _Vaclav Kotesovec_, Mar 18 2023 *)
%o A341782 (PARI) default(realprecision, 120);
%o A341782 a(n) = round(sqrt(prod(j=1, n, prod(k=1, n-1, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin(2*k*Pi/n)^2))));
%Y A341782 Main diagonal of A341738.
%Y A341782 Cf. A341478, A341535.
%K A341782 nonn
%O A341782 0,3
%A A341782 _Seiichi Manyama_, Feb 19 2021