A089004 Number of partitions of an n-element set that have at least one odd block.

1, 1, 5, 11, 52, 172, 877, 3761, 21147, 109419, 678570, 4063248, 27644437, 186525861, 1382958545, 10323844183, 82864869804, 675378319788, 5832742205057, 51386368744773, 474869816156751, 4486977535640087

Offset: 1

Author

Vladeta Jovovic, Nov 02 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A000110, A005046, A003724, A086543, A087137.

Programs

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,
       max(t, `if`(j=0, 0, irem(i, 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

With[{nn=30},CoefficientList[Series[Exp[Cosh[x]-1](Exp[Sinh[x]]-1),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 04 2018 *)

Formula

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