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A097762 Number of different partitions of the set {1, 2, ..., n} into an odd number of blocks such that each block contains at least 2 elements.

%I A097762 #12 Oct 08 2017 18:15:19
%S A097762 0,1,1,1,1,16,106,491,1919,7771,40261,264892,1871728,12988977,
%T A097762 88413417,612354549,4492798353,35529920764,299329573882,2625719242667,
%U A097762 23612697535919,216981233646783,2047084700918445,19952633715109592
%N A097762 Number of different partitions of the set {1, 2, ..., n} into an odd number of blocks such that each block contains at least 2 elements.
%H A097762 Alois P. Heinz, <a href="/A097762/b097762.txt">Table of n, a(n) for n = 1..500</a>
%F A097762 E.g.f.: sinh(exp(x)-x-1).
%e A097762 a(6)=16 since we can partition a set of six labeled elements into one non-singleton block in 1 way and into three non-singleton blocks (each necessarily of size 2) in 15 ways; thus a(6) = 1+15 = 16.
%p A097762 seq(coeff(series(sinh(exp(x)-x-1),x=0,25),x^i)*i!, i=1..24);
%p A097762 # second Maple program:
%p A097762 with(combinat):
%p A097762 b:= proc(n, i, t) option remember; `if`(n=0, t,
%p A097762       `if`(i<2, 0, add(multinomial(n, n-i*j, i$j)/j!*
%p A097762        b(n-i*j, i-1, irem(t+j, 2)), j=0..n/i)))
%p A097762     end:
%p A097762 a:= n-> b(n$2, 0):
%p A097762 seq(a(n), n=1..30);  # _Alois P. Heinz_, Mar 08 2015
%t A097762 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, 0]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Jan 10 2016, after _Alois P. Heinz_ *)
%Y A097762 Cf. A000296, A097763.
%K A097762 easy,nonn
%O A097762 1,6
%A A097762 Isabel C. Lugo (izzycat(AT)gmail.com), Aug 23 2004