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 A343788 #7 Apr 29 2021 18:51:24
%S A343788 1,1,3,13,75,540,4671,47125,543371,7048453,101589591,1610634433,
%T A343788 27856938387,521953586233,10532102378983,227699187663961,
%U A343788 5250934660206219,128659152359921997,3337861722359261475,91406502629924948053,2634888477782107003707,79751100251346500871481
%N A343788 Number of ordered partitions of an n-set without blocks of size 5.
%F A343788 E.g.f.: 1 / (2 + x^5/5! - exp(x)).
%p A343788 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A343788 `if`(j=5, 0, a(n-j)*binomial(n, j)), j=1..n))
%p A343788 end:
%p A343788 seq(a(n), n=0..21); # _Alois P. Heinz_, Apr 29 2021
%t A343788 nmax = 21; CoefficientList[Series[1/(2 + x^5/5! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A343788 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 5, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
%Y A343788 Cf. A000670, A032032, A337058, A337059, A343665, A343787, A343789, A343790, A343791, A343792, A343793.
%K A343788 nonn
%O A343788 0,3
%A A343788 _Ilya Gutkovskiy_, Apr 29 2021