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 A333882 #13 Sep 22 2023 12:18:13
%S A333882 1,1,1,1,1,1,2,8,29,85,211,464,1399,7801,45410,216581,853218,2896002,
%T A333882 11708734,79817500,615700986,4012571831,21538473686,98707812691,
%U A333882 501634082800,3983368886226,37404203343457,305886831698593,2069143637726674,11924094649669375
%N A333882 Expansion of e.g.f. exp(Sum_{k>=0} x^(5*k + 1) / (5*k + 1)!).
%C A333882 Number of partitions of n-set into blocks congruent to 1 mod 5.
%F A333882 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/5)} binomial(n-1,5*k) * a(n-5*k-1). - _Seiichi Manyama_, Sep 22 2023
%t A333882 nmax = 29; CoefficientList[Series[Exp[Sum[x^(5 k + 1)/(5 k + 1)!, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A333882 a[n_] := a[n] = Sum[Boole[MemberQ[{1}, Mod[k, 5]]] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 29}]
%t A333882 nmax = 30; CoefficientList[Series[Exp[x*HypergeometricPFQ[{}, {2/5, 3/5, 4/5, 6/5}, x^5/3125]], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Apr 15 2020 *)
%Y A333882 Cf. A000110, A003724, A306347, A333881, A333883.
%K A333882 nonn
%O A333882 0,7
%A A333882 _Ilya Gutkovskiy_, Apr 08 2020