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A096647
Number of partitions of an n-set with even number of even blocks.
2
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
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
Sequence in context: A076884 A138388 A138386 * A054109 A305256 A323613
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 14 2004
EXTENSIONS
More terms from Emeric Deutsch, Nov 16 2004
STATUS
approved