cp's OEIS Frontend

A343664 Number of partitions of an n-set without blocks of size 4.

%I A343664 #10 Apr 28 2021 20:59:44
%S A343664 1,1,2,5,14,47,173,702,3125,14910,76495,418035,2418397,14791597,
%T A343664 95093612,641094695,4521228732,33250447919,254585084539,2024995604762,
%U A343664 16702070759557,142642458681486,1259387604241013,11479967000116911,107910143688962037,1044735841257587203,10407104137208385924
%N A343664 Number of partitions of an n-set without blocks of size 4.
%H A343664 Alois P. Heinz, <a href="/A343664/b343664.txt">Table of n, a(n) for n = 0..581</a>
%F A343664 E.g.f.: exp(exp(x) - 1 - x^4/4!).
%F A343664 a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * Bell(n-4*k) / ((n-4*k)! * k! * (4!)^k).
%p A343664 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A343664       `if`(j=4, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
%p A343664     end:
%p A343664 seq(a(n), n=0..26);  # _Alois P. Heinz_, Apr 25 2021
%t A343664 nmax = 26; CoefficientList[Series[Exp[Exp[x] - 1 - x^4/4!], {x, 0, nmax}], x] Range[0, nmax]!
%t A343664 Table[n! Sum[(-1)^k BellB[n - 4 k]/((n - 4 k)! k! (4!)^k), {k, 0, Floor[n/4]}], {n, 0, 26}]
%t A343664 a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n - 1, k - 1]  a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 26}]
%Y A343664 Cf. A000110, A000296, A027338, A097514, A124504, A343665, A343666, A343667, A343668, A343669.
%K A343664 nonn
%O A343664 0,3
%A A343664 _Ilya Gutkovskiy_, Apr 25 2021