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 A375803 #12 Jan 05 2025 19:51:42
%S A375803 0,20,195,4420,72624,1347905,23877840,430583140,7712000835,
%T A375803 138485573876,2484341814240,44584372180225,800002107309600,
%U A375803 14355674602647860,257600625681170499,4622465972012379940,82946715695078486160,1488418904383171787585,26708590219470770907120
%N A375803 a(n) = Fibonacci(n-1) * Fibonacci(n+1) * Fibonacci(2*n-1) * Fibonacci(2*n+1).
%H A375803 Amiram Eldar, <a href="/A375803/b375803.txt">Table of n, a(n) for n = 1..798</a>
%H A375803 Hideyuki Ohtskua, proposer, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/AugAdvProb2024.pdf">Problem H-944</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 62, No. 3 (2024), p. 266.
%H A375803 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (13,104,-260,-260,104,13,-1).
%F A375803 a(n) = A059929(n-1) * A059929(2*n-1) = A059929(n-1) * A064170(n+2).
%F A375803 Sum_{n>=2} (-1)^n/a(n) = (5*sqrt(5) - 11)/4 = A374149 - 11/2 = 10 * A134944 - 4 (Ohtskua, 2024).
%F A375803 G.f.: -x^2*(-20+65*x+195*x^2-84*x^3-13*x^4+x^5) / ( (1+x)*(x^2-3*x+1)*(x^2-18*x+1)*(x^2+7*x+1) ). - _R. J. Mathar_, Aug 30 2024
%t A375803 a[n_] := Fibonacci[n-1] * Fibonacci[n+1] * Fibonacci[2*n-1] * Fibonacci[2*n+1]; Array[a, 20]
%o A375803 (PARI) a(n) = fibonacci(n-1) * fibonacci(n+1) * fibonacci(2*n-1) * fibonacci(2*n+1);
%Y A375803 Cf. A000045, A059929, A064170, A134944, A374149, A375804.
%K A375803 nonn,easy
%O A375803 1,2
%A A375803 _Amiram Eldar_, Aug 29 2024