A096579 Number of partitions of an n-set with exactly one even block.

0, 1, 3, 7, 25, 91, 329, 1415, 6297, 29431, 151085, 802099, 4506957, 26836083, 165586321, 1074740079, 7268876881, 50985776815, 372854157589, 2820244541675, 22087612114805, 179014336044171, 1495539626297689, 12894921568568999, 114481871464864825

Offset: 1

Author

Vladeta Jovovic, Aug 13 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..591

Crossrefs

Cf. A003724.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, t, add(
      `if`(t=1 and j::even, 0, binomial(n-1, j-1)*
       b(n-j, `if`(j::even, 1, t))), j=1..n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=1..30);  # Alois P. Heinz, May 10 2016

Mathematica

Drop[ Range[0, 24]! CoefficientList[ Series[ E^Sinh[x]*(Cosh[x] - 1), {x, 0, 24}], x], 1] (* Robert G. Wilson v, Aug 17 2004 *)

Formula

E.g.f.: exp(sinh(x))*(cosh(x)-1). More generally, e.g.f. for the number of partitions of n-set with exactly k even blocks is 1/k!*exp(sinh(x))*(cosh(x)-1)^k.

Extensions

More terms from Robert G. Wilson v, Aug 17 2004