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 A361608 #24 Jun 10 2024 10:31:58
%S A361608 1,924,48804,1337014,26622288,437049228,6295986235,82489361052,
%T A361608 1005444707211,11576481361732,127278262644918,1346951022678114,
%U A361608 13803666582387682,137633164619393268,1340161331495822661,12782144706910135480,119711031072135899781,1103157160378734314700,10019811250265958667288
%N A361608 a(n) = 7^n*(n+1)*(81*n^4+684*n^3+1401*n^2+434*n+40)/40.
%C A361608 The sequences A(n,k) = Sum_{j=0..n} Sum_{i=0..j} (-1)^(j-i) * binomial(n,j) * binomial(j,i) * binomial(j+k+(k+1)*i,j+k) are C-sequences for fixed integer k, here A(n,k=5) = a(n).
%H A361608 Project Euler, <a href="https://projecteuler.net/problem=831">Problem 831. Triple Product</a>
%H A361608 R. J. Mathar, <a href="https://arxiv.org/abs/2306.08022">On an alternating double sum of a triple product of aerated binomial coefficients</a>, arXiv:2306.08022 (2023)
%H A361608 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (42,-735,6860,-36015,100842,-117649).
%F A361608 G.f.: ( 1+882*x+10731*x^2-40474*x^3+36015*x^4 ) / (7*x-1)^6 .
%F A361608 a(n) = +42*a(n-1) -735*a(n-2) +6860*a(n-3) -36015*a(n-4) +100842*a(n-5) -117649*a(n-6).
%F A361608 D-finite with recurrence n*(81*n^4+360*n^3-165*n^2-640*n+404)*a(n) -7*(n+1)*(81*n^4+684*n^3+1401*n^2+434*n+40)*a(n-1)=0.
%t A361608 LinearRecurrence[{42,-735,6860,-36015,100842,-117649},{1,924,48804,1337014,26622288,437049228},20] (* _Harvey P. Dale_, May 29 2023 *)
%o A361608 (Python)
%o A361608 def A361608(n): return 7**n*(n*(n*(n*(n*(81*n + 765) + 2085) + 1835) + 474) + 40)//40 # _Chai Wah Wu_, Mar 17 2023
%Y A361608 Cf. A027471 (k=1), A361609 (k=2), A361610 (k=3).
%K A361608 nonn,easy
%O A361608 0,2
%A A361608 _R. J. Mathar_, Mar 17 2023