# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a070967 Showing 1-1 of 1 %I A070967 #19 Jun 19 2021 17:53:30 %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, Table of n, a(n) for n = 0..554 %H A070967 Index entries for linear recurrences with constant coefficients, signature (38,1691,-1728). %F A070967 G.f.: (1-36x-841x^2+288x^3)/((1-x)(1+27x)(1-64x)). 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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE