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 A344493 #4 May 21 2021 08:06:00
%S A344493 1,1,1,1,1,1,2,4,8,16,32,64,135,308,767,2059,5821,16963,50312,151189,
%T A344493 460981,1433634,4578748,15110212,51704075,183423444,672385222,
%U A344493 2534056116,9768179743,38357842713,153070136072,620275332697,2553688944713,10696223834397,45654239302087
%N A344493 a(n) = 1 + Sum_{k=0..n-6} binomial(n-5,k) * a(k).
%F A344493 G.f. A(x) satisfies: A(x) = (1 + x^5 * A(x/(1 - x))) / ((1 - x) * (1 + x^5)).
%t A344493 a[n_] := a[n] = 1 + Sum[Binomial[n - 5, k] a[k] , {k, 0, n - 6}]; Table[a[n], {n, 0, 34}]
%t A344493 nmax = 34; A[_] = 0; Do[A[x_] = (1 + x^5 A[x/(1 - x)])/((1 - x) (1 + x^5)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A344493 Cf. A000629, A210543, A344489, A344490, A344491, A344492.
%K A344493 nonn
%O A344493 0,7
%A A344493 _Ilya Gutkovskiy_, May 21 2021