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

%I A088142 #15 Apr 08 2016 06:39:42
%S A088142 3,10,50,116,560,1730,6123,30122,116908,507277,2492737,15328119,
%T A088142 56182092,441156796,2093130576,15965840718,77353276330,693400983344,
%U A088142 3517825829117,35126205660152,187347585491624,1952969742765476
%N A088142 Number of partitions of n-set with 2 block sizes.
%H A088142 Alois P. Heinz, <a href="/A088142/b088142.txt">Table of n, a(n) for n = 3..300</a>
%F A088142 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
%p A088142 with(numtheory): with(combinat):
%p A088142 a:= n-> add(add(add(multinomial(n, i$j, d$((n-i*j)/d))/j!/((n-i*j)/d)!,
%p A088142         d=select(x->x<i, divisors(n-i*j))), j=1..n/i), i=2..n-1):
%p A088142 seq(a(n), n=0..30);  # _Alois P. Heinz_, Feb 01 2014
%t A088142 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 *)
%Y A088142 Cf. A005772, A038041, A002133.
%Y A088142 Column k=2 of A208437.
%K A088142 nonn
%O A088142 3,1
%A A088142 _Vladeta Jovovic_, Nov 02 2003