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 A345456 #19 Aug 25 2022 13:49:16
%S A345456 1,22,859,25773,843756,26789257,859595529,27481113638,879683351911,
%T A345456 28146676447417,900729032983924,28822936611339453,922338323835136341,
%U A345456 29514778095285204502,944473434343229560419,30223143962480773595093,967140672636207153780796
%N A345456 a(n) = Sum_{k=0..n} binomial(5*n+2,5*k).
%H A345456 Seiichi Manyama, <a href="/A345456/b345456.txt">Table of n, a(n) for n = 0..500</a>
%H A345456 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,353,-32).
%F A345456 G.f.: (1 + x + 44*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
%F A345456 a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
%F A345456 a(n) = A139398(5*n+2).
%F A345456 a(n) = 2^(5*n + 3)/10 + ((-295 + 131*sqrt(5))/phi^(5*n) + (115 - 49*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 A345456 a[n_] := Sum[Binomial[5*n + 2, 5*k], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Jun 20 2021 *)
%t A345456 LinearRecurrence[{21,353,-32},{1,22,859},20] (* _Harvey P. Dale_, Aug 25 2022 *)
%o A345456 (PARI) a(n) = sum(k=0, n, binomial(5*n+2, 5*k));
%o A345456 (PARI) my(N=20, x='x+O('x^N)); Vec((1+x+44*x^2)/((1-32*x)*(1+11*x-x^2)))
%Y A345456 Sum_{k=0..n} binomial(b*n+c,b*k): A070782 (b=5,c=0), A345455 (b=5,c=1), this sequence (b=5,c=2), A345457 (b=5,c=3), A345458 (b=5,c=4).
%Y A345456 Cf. A139398.
%K A345456 nonn
%O A345456 0,2
%A A345456 _Seiichi Manyama_, Jun 20 2021