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.

A277352 a(n) = Product_{k=1..n} (2*k^2+1).

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%I A277352 #15 Mar 16 2023 15:52:13
%S A277352 1,3,27,513,16929,863379,63026667,6239640033,804913564257,
%T A277352 131200910973891,26371383105752091,6408246094697758113,
%U A277352 1851983121367652094657,627822278143634060088723,246734155310448185614868139,111277104045012131712305530689
%N A277352 a(n) = Product_{k=1..n} (2*k^2+1).
%C A277352 Guadalupe proves that a(n) is not square for n > 0. - _Charles R Greathouse IV_, Mar 16 2023
%H A277352 Russelle Guadalupe, <a href="https://arxiv.org/abs/2201.00501">Squares of the form Product_{k=1..n} (2k^2+l) with l odd</a>, arXiv:2201.00501 [math.NT], 2022.
%F A277352 a(n) ~ 2^(n+3/2) * n^(2*n+1) * sinh(Pi/sqrt(2)) / exp(2*n).
%t A277352 Table[Product[2*k^2+1, {k, 1, n}], {n, 0, 15}]
%o A277352 (PARI) a(n)=prod(k=1,n,2*k^2+1) \\ _Charles R Greathouse IV_, Mar 16 2023
%Y A277352 Cf. A101686, A277347, A277353, A277354.
%K A277352 nonn
%O A277352 0,2
%A A277352 _Vaclav Kotesovec_, Oct 10 2016