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

1,3

Links

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

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.

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 *)

Crossrefs

Cf. A003724.

Sequence in context: A287892 A343278 A002870 * A350650 A120540 A176829

Adjacent sequences: A096576 A096577 A096578 * A096580 A096581 A096582

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 13 2004

Extensions

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

Status

approved