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 A343789 #7 Apr 29 2021 18:53:39
%S A343789 1,1,3,13,75,541,4682,47279,545611,7083565,102182883,1621425829,
%T A343789 28067555607,526349480593,10629883138059,230009622202373,
%U A343789 5308749619032571,130186940173803053,3380385112758108315,92650130825921846941,2673020491585091254035,80974418589343644492805
%N A343789 Number of ordered partitions of an n-set without blocks of size 6.
%F A343789 E.g.f.: 1 / (2 + x^6/6! - exp(x)).
%p A343789 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A343789 `if`(j=6, 0, a(n-j)*binomial(n, j)), j=1..n))
%p A343789 end:
%p A343789 seq(a(n), n=0..21); # _Alois P. Heinz_, Apr 29 2021
%t A343789 nmax = 21; CoefficientList[Series[1/(2 + x^6/6! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A343789 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 6, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
%Y A343789 Cf. A000670, A032032, A337058, A337059, A343666, A343787, A343788, A343790, A343791, A343792, A343793.
%K A343789 nonn
%O A343789 0,3
%A A343789 _Ilya Gutkovskiy_, Apr 29 2021