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

0,3

Links

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

Formula

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

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

Example

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

Maple

G:=exp(exp(x)-1-x^3/6): Gser:=series(G, x=0, 30): seq(n!*coeff(Gser, x, n), n=0..26);
# Alternative:
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 *)

Prog

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

Crossrefs

Cf. A124503, A328153.

Sequence in context: A148171 A318644 A113774 * A056324 A056325 A345207

Adjacent sequences: A124501 A124502 A124503 * A124505 A124506 A124507

Keyword

nonn

Author

Emeric Deutsch, Nov 14 2006

Status

approved