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A088142 Number of partitions of n-set with 2 block sizes. 5
3, 10, 50, 116, 560, 1730, 6123, 30122, 116908, 507277, 2492737, 15328119, 56182092, 441156796, 2093130576, 15965840718, 77353276330, 693400983344, 3517825829117, 35126205660152, 187347585491624, 1952969742765476 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified April 3 14:34 EDT 2020. Contains 333197 sequences. (Running on oeis4.)