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A097763 Number of different partitions of the set {1, 2, ..., n} into an even number of blocks such that each block contains at least 2 elements. 2

%I

%S 0,0,0,3,10,25,56,224,1506,9951,57992,315425,1761552,11022180,

%T 78474748,603715831,4771273414,38070877273,309146434240,2598546954268,

%U 22887194502518,211388690471531,2031261113410564,20121026325645745

%N Number of different partitions of the set {1, 2, ..., n} into an even number of blocks such that each block contains at least 2 elements.

%C a(n) = A000296(n) - A097762(n).

%H Alois P. Heinz, <a href="/A097763/b097763.txt">Table of n, a(n) for n = 1..500</a>

%F Exponential generating function: cosh(exp(x)-x-1).

%e a(6)=25 since we can partition a set of six elements into two non-singleton blocks, either of sizes four and two (15 ways) or three and three (10 ways); a(6)=15+10=25.

%p seq(coeff(series(cosh(exp(x)-x-1),x=0,25),x^i)*i!, i=1..24);

%p # second Maple program:

%p with(combinat):

%p b:= proc(n, i, t) option remember; `if`(n=0, t,

%p `if`(i<2, 0, add(multinomial(n, n-i*j, i$j)/j!*

%p b(n-i*j, i-1, irem(t+j, 2)), j=0..n/i)))

%p end:

%p a:= n-> b(n$2, 1):

%p seq(a(n), n=1..30); # _Alois P. Heinz_, Mar 08 2015

%t multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i < 2, 0, Sum[multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!*b[n - i*j, i - 1, Mod[t + j, 2]], {j, 0, n/i}]]]; a[n_] := b[n, n, 1]; Table[a[n], {n, 1, 30}] (* _Jean-Fran├žois Alcover_, Jan 10 2016, after _Alois P. Heinz_ *)

%Y Cf. A000296, A097762.

%K easy,nonn

%O 1,4

%A Isabel C. Lugo (izzycat(AT)gmail.com), Aug 23 2004

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Last modified January 20 05:37 EST 2020. Contains 331067 sequences. (Running on oeis4.)