A114934 Number of connected (5,n)-hypergraphs (without empty edges and without multiple edges).
0, 0, 0, 21, 2773, 148365, 5878391, 204819447, 6721694469, 214306917321, 6736603947907, 210284186632443, 6541309609120385, 203129541349695597, 6302428271530970943, 195459285517696665759, 6060542952694406463421
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..670
- Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
Programs
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Mathematica
With[{nmax = 50}, CoefficientList[Series[(1/5!)*(Exp[31*x] - 5*Exp[16*x] - 10*Exp[15*x] - 10*Exp[10*x] + 20*Exp[9*x] + 40*Exp[8*x] + 65*Exp[7*x] - 30*Exp[6*x] - 96*Exp[5*x] - 45*Exp[4*x] + 20*Exp[3*x] + 50*Exp[2*x] + 24*Exp[x] - 24), {x, 0, nmax}], x] Range[0, nmax]!] (* G. C. Greubel, Oct 07 2017 *) -
PARI
x='x+O('x^50); concat([0,0,0], Vec(serlaplace((1/5!)*(exp(31*x) - 5*exp(16*x) - 10*exp(15*x) - 10*exp(10*x) + 20*exp(9*x) + 40*exp(8*x) + 65*exp(7*x) - 30*exp(6*x) - 96*exp(5*x) - 45*exp(4*x) + 20*exp(3*x) + 50*exp(2*x) + 24*exp(x) - 24)))) \\ G. C. Greubel, Oct 07 2017
Formula
E.g.f.: (1/5!)*(exp(31*x) - 5*exp(16*x) - 10*exp(15*x) - 10*exp(10*x) + 20*exp(9*x) + 40*exp(8*x) + 65*exp(7*x) - 30*exp(6*x) - 96*exp(5*x) - 45*exp(4*x) + 20*exp(3*x) + 50*exp(2*x) + 24*exp(x) - 24).