A096648 Number of partitions of an n-set with odd number of even blocks.

0, 1, 3, 7, 25, 106, 434, 2045, 10707, 57781, 338195, 2115664, 13796952, 95394573, 692462671, 5235101739, 41436754261, 341177640610, 2915100624274, 25866987547865, 237448494222575, 2252995117706961, 22078799199129799, 222971522853648704, 2319210969809731600

Offset

1,3

Links

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

Formula

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

a(2*n) = A024429(2*n) and a(2*n+1) = A024430(2*n+1). - Jonathan Vos Post, Oct 19 2005

a(n) = sum{k=0..n, if(mod(n-k,2)=1, A048993(n,k), 0)}. - Paul Barry, May 19 2006

Maple

with(combinat):
b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1,
      0, add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1,
      irem(t+`if`(irem(i, 2)=0, j, 0), 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<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i-1, Mod[t+If[Mod[i, 2] == 0, j, 0], 2]], {j, 0, n/i}]]]; a[n_] := b[n, n, 2]; Table[ a[n], {n, 1, 30}] (* Jean-François Alcover, May 13 2015, after Alois P. Heinz *)
With[{nn=30}, Rest[CoefficientList[Series[Exp[Sinh[x]]Sinh[Cosh[x]-1], {x, 0, nn}], x] Range[0, nn]!]] (* Harvey P. Dale, Sep 03 2016 *)

Crossrefs

Cf. A000701.

Cf. A024429, A024430, A096647.

Sequence in context: A352385 A133206 A054092 * A156100 A245115 A215772

Adjacent sequences: A096645 A096646 A096647 * A096649 A096650 A096651

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 14 2004

Extensions

More terms from Emeric Deutsch, Nov 16 2004

Status

approved