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A124504 Number of partitions of an n-set without blocks of size 3. 2
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 (list; graph; refs; listen; history; text; internal format)
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);

# second Maple program:

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1,

      `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)

       /j!*b(n-i*j, i-1), j=0..`if`(i=3, 0, n/i))))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015

MATHEMATICA

a[n_] := SeriesCoefficient[Exp[Exp[x]-1-x^3/6], {x, 0, n}]*n!; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois 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.

Sequence in context: A148171 A318644 A113774 * A056324 A056325 A103293

Adjacent sequences:  A124501 A124502 A124503 * A124505 A124506 A124507

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 14 2006

STATUS

approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)