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