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 A383719 #24 May 10 2025 11:28:26
%S A383719 1,70,5915,482664,39618670,3248730940,266442347522,21851425660680,
%T A383719 1792084691254935,146972777186757522,12053560080255418725,
%U A383719 988538895611708641200,81072243052956528402380,6648912468496274313591800,545291894670184984544154100,44720584275276797753993516592
%N A383719 a(n) = Pell(n) * Pell(n-1) * Pell(n-2) * Pell(n-3) * Pell(n-4) / 3480.
%H A383719 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (70,1015,-2436,-1015,70,1).
%F A383719 G.f.: x^5 * exp( Sum_{k>=1} Pell(6*k)/Pell(k) * x^k/k ).
%F A383719 G.f.: x^5 / ((1-2*x-x^2) * (1+14*x-x^2) * (1-82*x-x^2)).
%F A383719 a(n) = 70*a(n-1) + 1015*a(n-2) - 2436*a(n-3) - 1015*a(n-4) + 70*a(n-5) + a(n-6).
%F A383719 a(n) = (1 + sqrt(2))^(5*(n-5)) * q-binomial(n, 5, -(sqrt(2) - 1)^2).
%o A383719 (PARI) pell(n) = ([2, 1; 1, 0]^n)[2, 1];
%o A383719 p(n, k) = prod(j=0, k-1, pell(n-j));
%o A383719 a(n) = p(n, 5)/p(5, 5);
%o A383719 (Sage)
%o A383719 def a(n): return ((1+sqrt(2))^(5*(n-5))*q_binomial(n, 5, -(3-2*sqrt(2)))).simplify_full()
%Y A383719 Fifth column of triangle A099927.
%Y A383719 Cf. A000129.
%K A383719 nonn,easy
%O A383719 5,2
%A A383719 _Seiichi Manyama_, May 07 2025