A102287 Total number of even blocks in all partitions of n-set.

0, 1, 3, 13, 55, 256, 1274, 6791, 38553, 232171, 1477355, 9898780, 69621864, 512585529, 3940556611, 31560327945, 262805569159, 2271094695388, 20333574916690, 188322882941471, 1801737999086129, 17783472151154007, 180866601699482803, 1893373126840572056

Offset: 1

Author

Vladeta Jovovic, Feb 19 2005

Keywords

• easy
• nonn

Examples

			a(3)=3 because in the 5 (=A000110(3)) partitions 123, (12)/3, (13)/2, 1/(23) and 1/2/3 of {1,2,3} we have 3 blocks of even size (shown between parentheses).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..575

Crossrefs

Cf. A005493, A000296.

Programs

Maple

G:=(cosh(x)-1)*exp(exp(x)-1): Gser:=series(G,x=0,28): seq(n!*coeff(Gser,x^n),n=1..25); # Emeric Deutsch, Jun 22 2005
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, 0],
       add((p->(p+[0, `if`(i::odd, 0, j)*p[1]]))(
       b(n-i*j, i-1))*multinomial(n, n-i*j, i$j)/j!, j=0..n/i))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..30);  # Alois P. Heinz, Sep 16 2015

Mathematica

Range[0, nn]! CoefficientList[
  D[Series[Exp[y (Cosh[x] - 1) + Sinh[x]], {x, 0, nn}], y] /. y -> 1,  x]  (* Geoffrey Critzer, Aug 28 2012 *)

Formula

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

Extensions

More terms from Emeric Deutsch, Jun 22 2005