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 A343667 #7 Apr 25 2021 20:07:53
%S A343667 1,1,2,5,15,52,203,876,4132,21075,115375,673620,4172413,27296089,
%T A343667 187891174,1356343385,10238632307,80615222404,660560758879,
%U A343667 5621465069117,49594663447612,452846969975391,4273130715906123,41612346388251187,417668648929556073,4315893703814296053
%N A343667 Number of partitions of an n-set without blocks of size 7.
%F A343667 E.g.f.: exp(exp(x) - 1 - x^7/7!).
%F A343667 a(n) = n! * Sum_{k=0..floor(n/7)} (-1)^k * Bell(n-7*k) / ((n-7*k)! * k! * (7!)^k).
%p A343667 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A343667 `if`(j=7, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
%p A343667 end:
%p A343667 seq(a(n), n=0..25); # _Alois P. Heinz_, Apr 25 2021
%t A343667 nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^7/7!], {x, 0, nmax}], x] Range[0, nmax]!
%t A343667 Table[n! Sum[(-1)^k BellB[n - 7 k]/((n - 7 k)! k! (7!)^k), {k, 0, Floor[n/7]}], {n, 0, 25}]
%t A343667 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 7, 0, Binomial[n - 1, k - 1] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]
%Y A343667 Cf. A000110, A000296, A027341, A097514, A124504, A343664, A343665, A343666, A343668, A343669.
%K A343667 nonn
%O A343667 0,3
%A A343667 _Ilya Gutkovskiy_, Apr 25 2021