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 A343671 #6 Jul 25 2023 08:39:19
%S A343671 1,1,2,5,15,52,203,877,4140,21147,115974,678559,4213465,27643007,
%T A343671 190884307,1382802389,10478516523,82847813908,681895648039,
%U A343671 5830788687491,51702731250650,474630475600569,4503991075480297,44120379612630694,445584481578266277,4634070027874688433
%N A343671 Number of partitions of an n-set without blocks of size 10.
%F A343671 E.g.f.: exp(exp(x) - 1 - x^10/10!).
%F A343671 a(n) = n! * Sum_{k=0..floor(n/10)} (-1)^k * Bell(n-10*k) / ((n-10*k)! * k! * (10!)^k).
%p A343671 a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
%p A343671 j=10, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
%p A343671 end:
%p A343671 seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 25 2023
%t A343671 nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^10/10!], {x, 0, nmax}], x] Range[0, nmax]!
%t A343671 Table[n! Sum[(-1)^k BellB[n - 10 k]/((n - 10 k)! k! (10!)^k), {k, 0, Floor[n/10]}], {n, 0, 25}]
%t A343671 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 10, 0, Binomial[n - 1, k - 1] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]
%Y A343671 Cf. A000110, A000296, A027344, A097514, A124504, A343664, A343665, A343666, A343667, A343668, A343669.
%K A343671 nonn
%O A343671 0,3
%A A343671 _Ilya Gutkovskiy_, Apr 25 2021