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 A345455 #23 Jul 20 2021 17:58:33
%S A345455 1,7,474,12393,427351,13333932,430470899,13733091643,439924466026,
%T A345455 14072420067757,450374698997499,14411355379952868,461170414282959151,
%U A345455 14757375158697584607,472236871202375365274,15111570273013075344193,483570355262634763462351
%N A345455 a(n) = Sum_{k=0..n} binomial(5*n+1,5*k).
%H A345455 Seiichi Manyama, <a href="/A345455/b345455.txt">Table of n, a(n) for n = 0..500</a>
%H A345455 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,353,-32).
%F A345455 G.f.: (1 - 14*x - 26*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
%F A345455 a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
%F A345455 a(n) = A139398(5*n+1).
%F A345455 a(n) = 2^(5*n + 2)/10 + ((-475 + 213*sqrt(5))/phi^(5*n) - ( 65 - 33*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 A345455 a[n_] := Sum[Binomial[5*n + 1, 5*k], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Jun 20 2021 *)
%t A345455 LinearRecurrence[{21,353,-32},{1,7,474},20] (* _Harvey P. Dale_, Jul 20 2021 *)
%o A345455 (PARI) a(n) = sum(k=0, n, binomial(5*n+1, 5*k));
%o A345455 (PARI) my(N=20, x='x+O('x^N)); Vec((1-14*x-26*x^2)/((1-32*x)*(1+11*x-x^2)))
%Y A345455 Sum_{k=0..n} binomial(b*n+c,b*k): A082311 (b=3,c=1), A090407 (b=4,c=1), A070782 (b=5,c=0), this sequence (b=5,c=1), A345456 (b=5,c=2), A345457 (b=5,c=3), A345458 (b=5,c=4).
%Y A345455 Cf. A139398.
%K A345455 nonn
%O A345455 0,2
%A A345455 _Seiichi Manyama_, Jun 20 2021