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

1, 1, 2, 4, 11, 32, 113, 422, 1788, 8015, 39435, 204910, 1144377, 6722107, 41877722, 273328660, 1875326627, 13427171644, 100415636519, 780856389454, 6312398830812, 52891894374481, 459022366424253, 4117482357137214, 38140612800271305, 364280428671552453, 3584042687233836274

Offset: 0

Author

Emeric Deutsch, Nov 14 2006

Keywords

• nonn

Examples

			a(3)=4 because if the set is {1,2,3}, then we have 1|2|3, 1|23, 12|3 and 13|2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A124503, A328153.

Programs

Maple

G:=exp(exp(x)-1-x^3/6): Gser:=series(G,x=0,30): seq(n!*coeff(Gser,x,n),n=0..26);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(
     `if`(j=3, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015, revised, Jun 24 2022

Mathematica

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 *)

PARI

x='x+O('x^66); Vec(serlaplace( exp(exp(x)-1-x^3/6) ) ) \\ Joerg Arndt, Jan 19 2015

Formula

E.g.f.: exp(exp(x)-1-x^3/6).

a(n) = A124503(n,0).