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 A352428 #11 Mar 23 2022 13:00:29
%S A352428 1,1,2,6,25,130,810,5881,48806,455706,4727881,53955682,671730246,
%T A352428 9059714665,131588822822,2047796305470,33992509701721,599526848094850,
%U A352428 11195864285933682,220692569175568729,4579248276057441926,99767702172338210898,2277136869014579978473,54336724559407913237122
%N A352428 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(n-3*k-1).
%H A352428 Seiichi Manyama, <a href="/A352428/b352428.txt">Table of n, a(n) for n = 0..447</a>
%F A352428 E.g.f.: 1 / (1 - Sum_{k>=0} x^(3*k+1) / (3*k+1)!).
%t A352428 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[n - 3 k - 1], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 23}]
%t A352428 nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(3 k + 1)/(3 k + 1)!, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%o A352428 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+1)/(3*k+1)!)))) \\ _Seiichi Manyama_, Mar 23 2022
%Y A352428 Cf. A000670, A006154, A243664, A291973, A333881, A352429, A352430.
%K A352428 nonn
%O A352428 0,3
%A A352428 _Ilya Gutkovskiy_, Mar 16 2022