A088142 Number of partitions of n-set with 2 block sizes.

3, 10, 50, 116, 560, 1730, 6123, 30122, 116908, 507277, 2492737, 15328119, 56182092, 441156796, 2093130576, 15965840718, 77353276330, 693400983344, 3517825829117, 35126205660152, 187347585491624, 1952969742765476

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..300

Formula

E.g.f.: (G(x)^2-H(x))/2 where G(x) = Sum {k>=1} (exp(x^k/k!)-1) and H(x) = Sum {k>=1} (exp(x^k/k!)-1)^2. - Vladeta Jovovic, Sep 18 2007

Maple

with(numtheory): with(combinat):
a:= n-> add(add(add(multinomial(n, i$j, d$((n-i*j)/d))/j!/((n-i*j)/d)!,
        d=select(x->x<i, divisors(n-i*j))), j=1..n/i), i=2..n-1):
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 01 2014

Mathematica

max = 25; G[x_] = Sum[Exp[x^k/k!]-1, {k, 1, max}]; H[x_] = Sum[(Exp[x^k/k!]-1)^2, {k, 1, max}]; Drop[CoefficientList[(G[x]^2-H[x])/2 + O[x]^max, x]*Range[0, max-1]!, 3] (* Jean-François Alcover, Jul 01 2015 *)

Crossrefs

Cf. A005772, A038041, A002133.

Column k=2 of A208437.

Sequence in context: A054381 A102088 A297295 * A276028 A209902 A049370

Adjacent sequences: A088139 A088140 A088141 * A088143 A088144 A088145

Keyword

nonn

Author

Vladeta Jovovic, Nov 02 2003

Status

approved