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Number of connected (3,n)-hypergraphs (without empty edges and without multiple edges).
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%I #11 Dec 17 2022 08:25:26

%S 0,0,1,25,267,2265,17471,128765,927067,6591505,46545591,327428805,

%T 2298406067,16114352345,112902172111,790721005645,5536667136267,

%U 38763140938785,271367842141031,1899678231827285,13298160713181667

%N Number of connected (3,n)-hypergraphs (without empty edges and without multiple edges).

%H G. C. Greubel, <a href="/A114932/b114932.txt">Table of n, a(n) for n = 0..1000</a>

%H Goran Kilibarda and Vladeta Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.

%F E.g.f.: (1/3!)*(exp(7*x)-3*exp(4*x)-exp(3*x)+3*exp(2*x)+2*exp(x)-2).

%t With[{nmax = 50}, CoefficientList[Series[(1/3!)*(Exp[7*x] - 3*Exp[4*x] - Exp[3*x] + 3*Exp[2*x] + 2*Exp[x] - 2), {x, 0, nmax}], x] Range[0, nmax]!] (* _G. C. Greubel_, Oct 07 2017 *)

%o (PARI) x='x+O('x^50); concat([0,0], Vec(serlaplace((1/3!)*(exp(7*x)-3*exp(4*x)-exp(3*x)+3*exp(2*x)+2*exp(x)-2)))) \\ _G. C. Greubel_, Oct 07 2017

%Y Cf. A002501, A002502, A093732, A093733.

%Y Cf. A114933, A114934, A114935, A114936, A114937.

%K easy,nonn

%O 0,4

%A Goran Kilibarda and _Vladeta Jovovic_, Jan 08 2006