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 A070782 #30 Aug 14 2025 03:15:23
%S A070782 1,2,254,6008,215766,6643782,215492564,6863694378,219993856006,
%T A070782 7035859329512,225191238869774,7205634556190798,230585685502492596,
%U A070782 7378682274243863442,236118494435702913134,7555784484021765207768,241785184867484394069286,7737125013254912900576822
%N A070782 a(n) = Sum_{k=0..n} binomial(5*n,5*k).
%H A070782 Seiichi Manyama, <a href="/A070782/b070782.txt">Table of n, a(n) for n = 0..664</a>
%H A070782 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,353,-32).
%F A070782 a(n) = (1/5)*32^n + (2/5)*(-11/2 + (5/2)*sqrt(5))^n + (2/5)*(-11/2 - (5/2)*sqrt(5))^n.
%F A070782 Let b(n) = a(n) - 2^(5n)/5; then b(n) + 11*b(n-1) - b(n-2) = 0. - _Benoit Cloitre_, May 27 2004
%F A070782 From _Colin Barker_, May 27 2019: (Start)
%F A070782 G.f.: (1 - 19*x - 141*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
%F A070782 a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
%F A070782 (End)
%t A070782 LinearRecurrence[{21,353,-32},{1,2,254},20] (* _Harvey P. Dale_, Jun 18 2023 *)
%o A070782 (PARI) a(n)=sum(k=0,n,binomial(5*n,5*k))
%o A070782 (PARI) Vec((1 - 19*x - 141*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)) + O(x^20)) \\ _Colin Barker_, May 27 2019
%Y A070782 Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), this sequence (b=5), A070967 (b=6), A094211 (b=7), A070832 (b=8), A094213 (b=9), A070833 (b=10).
%K A070782 easy,nonn
%O A070782 0,2
%A A070782 Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002