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 A094211 #38 Aug 14 2025 03:22:47
%S A094211 1,2,3434,232562,42484682,4653367842,644032289258,79450506979090,
%T A094211 10353832741654602,1313930226050847938,168883831255263816554,
%U A094211 21573903987107973878962,2764126124873404346104778,353643666623193292098680930,45276535087893983968685884906
%N A094211 a(n) = Sum_{k=0..n} binomial(7*n,7*k).
%H A094211 Seiichi Manyama, <a href="/A094211/b094211.txt">Table of n, a(n) for n = 0..474</a>
%H A094211 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (71,7585,-36991,-128).
%F A094211 Let b(n) = a(n) - 2^(7n)/7; then b(n) + 57*b(n-1) - 289*b(n-2) - b(n-3) = 0.
%F A094211 a(n) = 71*a(n-1) + 7585*a(n-2) - 36991*a(n-3) - 128*a(n-4); a(0)=1, a(1)=2, a(2)=3434, a(3)=232562. - _Harvey P. Dale_, May 06 2012
%F A094211 G.f.: (1 - 69*x - 4293*x^2 + 10569*x^3) / ((1 - 128*x)*(1 + 57*x - 289*x^2 - x^3)). - _Colin Barker_, May 27 2019
%F A094211 a(n) = (1 + 2*(s*(3 - 4*s^2))^(7*n) + 2*(-1)^n*((1 - 2*s^2)^(7*n) + s^(7*n))) * 2^(7*n)/7, where s = sin(Pi/14). - _Vaclav Kotesovec_, Apr 17 2023
%p A094211 A094211:=n->add(binomial(7*n,7*k), k=0..n): seq(A094211(n), n=0..20); # _Wesley Ivan Hurt_, Feb 16 2017
%t A094211 Table[Sum[Binomial[7n,7k],{k,0,n}],{n,0,20}] (* or *) LinearRecurrence[ {71,7585,-36991,-128},{1,2,3434,232562},20] (* _Harvey P. Dale_, May 06 2012 *)
%o A094211 (PARI) a(n)=sum(k=0,n,binomial(7*n,7*k))
%Y A094211 Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), A070782 (b=5), A070967 (b=6), this sequence (b=7), A070832 (b=8), A094213 (b=9), A070833 (b=10).
%K A094211 nonn,easy
%O A094211 0,2
%A A094211 _Benoit Cloitre_, May 27 2004