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 A070967 #29 Aug 14 2025 03:59:06
%S A070967 1,2,926,37130,2973350,174174002,11582386286,729520967450,
%T A070967 47006639297270,2999857885752002,192222214478506046,
%U A070967 12295976362284182570,787111112023373201990,50370558298891875954002,3223838658635388303336206,206322355109994528871954490
%N A070967 a(n) = Sum_{k=0..n} binomial(6*n,6*k).
%D A070967 Matthijs Coster, Supercongruences, Thesis, Jun 08, 1988.
%H A070967 Seiichi Manyama, <a href="/A070967/b070967.txt">Table of n, a(n) for n = 0..554</a>
%H A070967 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (38,1691,-1728).
%F A070967 G.f.: (1-36x-841x^2+288x^3)/((1-x)*(1+27x)*(1-64x)).
%F A070967 a(n) = ((-27)^n + 1)/3 + (64^n + 0^n)/6.
%F A070967 Let b(n) = a(n)-2^(6n)/6 then b(n)+26*b(n-1)-27*b(n-2) = 0. - _Benoit Cloitre_, May 27 2004
%t A070967 Table[Sum[Binomial[6n,6k],{k,0,n}],{n,0,20}] (* or *) LinearRecurrence[ {38,1691,-1728},{1,2,926,37130},30] (* _Harvey P. Dale_, Jun 19 2021 *)
%o A070967 (PARI) a(n)=sum(k=0,n,binomial(6*n,6*k))
%o A070967 (PARI) a(n)=if(n<0,0,(2*(-27)^n+2+64^n+0^n)/6)
%o A070967 (PARI) a(n)=if(n<0,0,polsym(x*(x-64)*(x+27)^2*(x-1)^2,n)[n+1]/6)
%Y A070967 Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), A070782 (b=5), this sequence (b=6), A094211 (b=7), A070832 (b=8), A094213 (b=9), A070833 (b=10).
%K A070967 easy,nonn
%O A070967 0,2
%A A070967 Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 16 2002