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 A345457 #19 Jun 20 2021 08:40:51
%S A345457 1,57,1574,53143,1669801,53774932,1717012749,54986385093,
%T A345457 1759098789526,56296324109907,1801425114687749,57646238657975068,
%U A345457 1844672594930734801,59029601136140621857,1888946370232447241574,60446293452901248074943
%N A345457 a(n) = Sum_{k=0..n} binomial(5*n+3,5*k).
%H A345457 Seiichi Manyama, <a href="/A345457/b345457.txt">Table of n, a(n) for n = 0..500</a>
%H A345457 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,353,-32).
%F A345457 G.f.: (1 + 36*x + 24*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)).
%F A345457 a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2.
%F A345457 a(n) = A139398(5*n+3).
%F A345457 a(n) = 2^(5*n + 4)/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 A345457 a[n_] := Sum[Binomial[5*n + 3, 5*k], {k, 0, n}]; Array[a, 16, 0] (* _Amiram Eldar_, Jun 20 2021 *)
%o A345457 (PARI) a(n) = sum(k=0, n, binomial(5*n+3, 5*k));
%o A345457 (PARI) my(N=20, x='x+O('x^N)); Vec((1+36*x+24*x^2)/((1-32*x)*(1+11*x-x^2)))
%Y A345457 Sum_{k=0..n} binomial(b*n+c,b*k): A090408 (b=4,c=3), A070782 (b=5,c=0), A345455 (b=5,c=1), A345456 (b=5,c=2), this sequence (b=5,c=3), A345458 (b=5,c=4).
%Y A345457 Cf. A139398.
%K A345457 nonn
%O A345457 0,2
%A A345457 _Seiichi Manyama_, Jun 20 2021