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A124504 Number of partitions of an n-set without blocks of size 3.

%I A124504 #15 Jun 24 2022 10:15:21
%S A124504 1,1,2,4,11,32,113,422,1788,8015,39435,204910,1144377,6722107,
%T A124504 41877722,273328660,1875326627,13427171644,100415636519,780856389454,
%U A124504 6312398830812,52891894374481,459022366424253,4117482357137214,38140612800271305,364280428671552453,3584042687233836274
%N A124504 Number of partitions of an n-set without blocks of size 3.
%H A124504 Alois P. Heinz, <a href="/A124504/b124504.txt">Table of n, a(n) for n = 0..500</a>
%F A124504 E.g.f.: exp(exp(x)-1-x^3/6).
%F A124504 a(n) = A124503(n,0).
%e A124504 a(3)=4 because if the set is {1,2,3}, then we have 1|2|3, 1|23, 12|3 and 13|2.
%p A124504 G:=exp(exp(x)-1-x^3/6): Gser:=series(G,x=0,30): seq(n!*coeff(Gser,x,n),n=0..26);
%p A124504 # second Maple program:
%p A124504 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A124504      `if`(j=3, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
%p A124504     end:
%p A124504 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 08 2015, revised, Jun 24 2022
%t A124504 a[n_] := SeriesCoefficient[Exp[Exp[x]-1-x^3/6], {x, 0, n}]*n!; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 13 2015 *)
%o A124504 (PARI) x='x+O('x^66); Vec(serlaplace( exp(exp(x)-1-x^3/6) ) ) \\ _Joerg Arndt_, Jan 19 2015
%Y A124504 Cf. A124503, A328153.
%K A124504 nonn
%O A124504 0,3
%A A124504 _Emeric Deutsch_, Nov 14 2006