A096619 Number of partitions of a 2*n-element set with exactly two odd blocks.

1, 10, 136, 2500, 59671, 1786060, 65222431, 2843052040, 145349748316, 8590361117290, 579887365929301, 44257224641241160, 3785653479578940061, 360188281690273321750, 37868568207290527576096, 4373779619483505303462160, 552095790104596359907313731

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..250

Formula

E.g.f.: 1/2*exp(cosh(x)-1)*(sinh(x))^2. More generally, number of partitions of an n-element set with exactly k odd blocks is 1/k!*exp(cosh(x)-1)*(sinh(x))^k.

Maple

with(combinat):
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(i<1 or t<0, 0, add(multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i-1, t-`if`(irem(i, 2)=1, j, 0) ), j=0..n/i)))
    end:
a:= n-> b(2*n$2, 2):
seq(a(n), n=1..20);  # 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, If[t == 0, 1, 0], If[i<1 || t<0, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i-1, t-If[Mod[i, 2] == 1, j, 0]], {j, 0, n/i}]]]; a[n_] := b[2*n, 2*n, 2]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, May 13 2015, after Alois P. Heinz *)

Crossrefs

Cf. A005046.

Sequence in context: A026244 A371405 A261503 * A276131 A003377 A371394

Adjacent sequences: A096616 A096617 A096618 * A096620 A096621 A096622

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 14 2004

Extensions

More terms from Emeric Deutsch, Nov 16 2004

Status

approved