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A097514 Number of partitions of an n-set without blocks of size 2. 9
1, 1, 1, 2, 6, 17, 53, 205, 871, 3876, 18820, 99585, 558847, 3313117, 20825145, 138046940, 959298572, 6974868139, 52972352923, 419104459913, 3446343893607, 29405917751526, 259930518212766, 2376498296500063, 22441988298860757 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n, 2*k)*(2*k-1)!!*Bell(n-2*k). E.g.f.: exp(exp(x)-1-x^2/2). More generally, e.g.f. for number of partitions of an n-set which contain exactly q blocks of size p is x^(p*q)/(q!*p!^q)*exp(exp(x)-1-x^p/p!).

MAPLE

g:=exp(exp(x)-1-x^2/2): gser:=series(g, x=0, 31): 1, seq(n!*coeff(gser, x^n), n=1..29); # Emeric Deutsch, Nov 18 2004

# second Maple program:

a:= proc(n) option remember; `if`(n=0, 1, add(`if`(

       j=2, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 18 2015

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, Sum[If[j == 2, 0, a[n-j]*Binomial[n-1, j-1]], {j, 1, n}]]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 13 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A000296, A327885.

Sequence in context: A148452 A307975 A148453 * A108630 A338735 A161408

Adjacent sequences:  A097511 A097512 A097513 * A097515 A097516 A097517

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 26 2004

EXTENSIONS

More terms from Emeric Deutsch, Nov 18 2004

STATUS

approved

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Last modified April 12 19:50 EDT 2021. Contains 342932 sequences. (Running on oeis4.)