A096647 Number of partitions of an n-set with even number of even blocks.

1, 1, 1, 2, 8, 27, 97, 443, 2095, 10440, 58194, 340375, 2097933, 13847485, 95504749, 690495874, 5245040408, 41428115543, 340899165549, 2917641580783, 25857170687507, 237421321934176, 2253720620740362, 22073206655954547, 222987346441156585, 2319379362420267753

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

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

a(n) = sum{k=0..n, if(mod(n-k,2)=0, A048993(n,k), 0)}. - Paul Barry, May 19 2006

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,
      irem(t+`if`(irem(i, 2)=0, j, 0), 2)), j=0..n/i)))
    end:
a:= n-> b(n$2, 1):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015

Mathematica

a[n_] := Sum[If[Mod[n-k, 2] == 0, StirlingS2[n, k], 0], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 16 2015, after Paul Barry *)

Crossrefs

Cf. A046682, A096648.

Sequence in context: A076884 A138388 A138386 * A054109 A305256 A323613

Adjacent sequences: A096644 A096645 A096646 * A096648 A096649 A096650

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 14 2004

Extensions

More terms from Emeric Deutsch, Nov 16 2004

Status

approved