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 A343669 #6 Apr 25 2021 20:08:06
%S A343669 1,1,2,5,15,52,203,877,4140,21146,115965,678460,4212497,27633712,
%T A343669 190795218,1381942530,10470109267,82764226404,681048663329,
%U A343669 5822029128397,51610194855972,473631475252041,4492967510009533,43996047374513046,444151309687221889,4617189912288741028
%N A343669 Number of partitions of an n-set without blocks of size 9.
%F A343669 E.g.f.: exp(exp(x) - 1 - x^9/9!).
%F A343669 a(n) = n! * Sum_{k=0..floor(n/9)} (-1)^k * Bell(n-9*k) / ((n-9*k)! * k! * (9!)^k).
%p A343669 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A343669 `if`(j=9, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
%p A343669 end:
%p A343669 seq(a(n), n=0..25); # _Alois P. Heinz_, Apr 25 2021
%t A343669 nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^9/9!], {x, 0, nmax}], x] Range[0, nmax]!
%t A343669 Table[n! Sum[(-1)^k BellB[n - 9 k]/((n - 9 k)! k! (9!)^k), {k, 0, Floor[n/9]}], {n, 0, 25}]
%t A343669 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 9, 0, Binomial[n - 1, k - 1] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]
%Y A343669 Cf. A000110, A000296, A027343, A097514, A124504, A343664, A343665, A343666, A343667, A343668.
%K A343669 nonn
%O A343669 0,3
%A A343669 _Ilya Gutkovskiy_, Apr 25 2021