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.

0, 1, 1, 1, 1, 16, 106, 491, 1919, 7771, 40261, 264892, 1871728, 12988977, 88413417, 612354549, 4492798353, 35529920764, 299329573882, 2625719242667, 23612697535919, 216981233646783, 2047084700918445, 19952633715109592

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

Formula

E.g.f.: sinh(exp(x)-x-1).

Example

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.

Maple

seq(coeff(series(sinh(exp(x)-x-1), x=0, 25), x^i)*i!, i=1..24);
# second Maple program:
with(combinat):
b:= proc(n, i, t) option remember; `if`(n=0, t,
      `if`(i<2, 0, add(multinomial(n, n-i*j, i$j)/j!*
       b(n-i*j, i-1, irem(t+j, 2)), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=1..30);  # Alois P. Heinz, Mar 08 2015

Mathematica

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 *)

Crossrefs

Cf. A000296, A097763.

Sequence in context: A195806 A081588 A276159 * A297610 A083469 A224160

Adjacent sequences: A097759 A097760 A097761 * A097763 A097764 A097765

Keyword

easy,nonn

Author

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

Status

approved