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.

A340167 a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 + sin(i*Pi/(2*n))^2 * sin(j*Pi/(2*n))^2).

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%I A340167 #19 Jan 05 2021 08:52:49
%S A340167 1,20,153425,450075709440,504979178328238519521,
%T A340167 216703205118496785026106198144000,
%U A340167 35568160616301682717925992221900586646216066081,2232861039051291914755952483706805051795013026559178904468193280
%N A340167 a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 + sin(i*Pi/(2*n))^2 * sin(j*Pi/(2*n))^2).
%F A340167 a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 + cos(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2).
%F A340167 a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 + sin(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2).
%F A340167 a(n) ~ 2^(4*n^2 - 6*n + 17/4) * (sqrt(2) - 1)^(2*n) * exp(4*A340350*n^2/Pi^2). - _Vaclav Kotesovec_, Jan 05 2021
%t A340167 Table[4^(2*(n-1)^2) * Product[Product[1 + Sin[i*Pi/(2*n)]^2 * Sin[j*Pi/(2*n)]^2, {i, 1, n-1}], {j, 1, n-1}], {n, 1, 10}] // Round (* _Vaclav Kotesovec_, Dec 31 2020 *)
%o A340167 (PARI) default(realprecision, 120);
%o A340167 {a(n) = round(4^(2*(n-1)^2)*prod(i=1, n-1, prod(j=1, n-1, 1+(sin(i*Pi/(2*n))*sin(j*Pi/(2*n)))^2)))}
%Y A340167 Cf. A340165, A340166.
%K A340167 nonn
%O A340167 1,2
%A A340167 _Seiichi Manyama_, Dec 30 2020