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 A343792 #7 Apr 29 2021 19:05:33
%S A343792 1,1,3,13,75,541,4683,47293,545835,7087260,102247543,1622632133,
%T A343792 28091557915,526858128161,10641337741219,230283060907913,
%U A343792 5315651289289195,130370674248854021,3385532005327322503,92801507648842580769,2677685300845992661475,81124743440296074264381
%N A343792 Number of ordered partitions of an n-set without blocks of size 9.
%F A343792 E.g.f.: 1 / (2 + x^9/9! - exp(x)).
%p A343792 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A343792 `if`(j=9, 0, a(n-j)*binomial(n, j)), j=1..n))
%p A343792 end:
%p A343792 seq(a(n), n=0..21); # _Alois P. Heinz_, Apr 29 2021
%t A343792 nmax = 21; CoefficientList[Series[1/(2 + x^9/9! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A343792 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 9, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
%Y A343792 Cf. A000670, A032032, A337058, A337059, A343669, A343787, A343788, A343789, A343790, A343791, A343793.
%K A343792 nonn
%O A343792 0,3
%A A343792 _Ilya Gutkovskiy_, Apr 29 2021