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

1,3

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A149525 A149526 A249075 * A197958 A094107 A107009

Adjacent sequences: A089001 A089002 A089003 * A089005 A089006 A089007

Keyword

nonn

Author

Vladeta Jovovic, Nov 02 2003

Status

approved