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 A345458 #21 Oct 29 2023 12:42:21
%S A345458 1,127,3004,107883,3321891,107746282,3431847189,109996928003,
%T A345458 3517929664756,112595619434887,3602817278095399,115292842751246298,
%U A345458 3689341137121931721,118059247217851456567,3777892242010882603884,120892592433742197034643
%N A345458 a(n) = Sum_{k=0..n} binomial(5*n+4,5*k).
%H A345458 Seiichi Manyama, <a href="/A345458/b345458.txt">Table of n, a(n) for n = 0..500</a>
%H A345458 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,353,-32).
%F A345458 G.f.: (1 + 106*x - 16*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
%F A345458 a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
%F A345458 a(n) = A139398(5*n+4).
%F A345458 a(n) = 2^(5*n + 5)/10 + ((2015 - 901*sqrt(5))/phi^(5*n) - (35 + sqrt(5))*(-1)^n*phi^(5*n)) / (10*(41*sqrt(5)-90)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Jun 20 2021
%t A345458 a[n_] := Sum[Binomial[5*n + 4, 5*k], {k, 0, n}]; Array[a, 16, 0] (* _Amiram Eldar_, Jun 20 2021 *)
%t A345458 Total/@Table[Binomial[5n+4,5k],{n,0,20},{k,0,n}] (* or *) LinearRecurrence[{21,353,-32},{1,127,3004},30] (* _Harvey P. Dale_, Oct 29 2023 *)
%o A345458 (PARI) a(n) = sum(k=0, n, binomial(5*n+4, 5*k));
%o A345458 (PARI) my(N=20, x='x+O('x^N)); Vec((1+106*x-16*x^2)/((1-32*x)*(1+11*x-x^2)))
%Y A345458 Sum_{k=0..n} binomial(b*n+c,b*k): A070782 (b=5,c=0), A345455 (b=5,c=1), A345456 (b=5,c=2), A345457 (b=5,c=3), this sequence (b=5,c=4).
%Y A345458 Cf. A139398.
%K A345458 nonn
%O A345458 0,2
%A A345458 _Seiichi Manyama_, Jun 20 2021