A114933 Number of connected (4,n)-hypergraphs (without empty edges and without multiple edges).

0, 0, 0, 32, 1094, 23055, 405475, 6575842, 102567444, 1569195485, 23775369725, 358461659952, 5391042181294, 80974624209115, 1215462744452775, 18238484835400862, 273628186560143144, 4104820038944901945

Offset: 0

Author

Goran Kilibarda and Vladeta Jovovic, Jan 08 2006

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..845
• Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

Crossrefs

Cf. A002501, A002502, A093732, A093732, A114934, A114935, A114936, A114937.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[(1/4!)*(Exp[15*x] - 4*Exp[8*x] - 6*Exp[7*x] - 3*Exp[6*x] + 12*Exp[5*x] + 12*Exp[4*x] - Exp[3*x] - 11*Exp[2*x] - 6*Exp[x] + 6), {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((1/4!)*(exp(15*x)-4*exp(8*x)-6*exp(7*x)-3*exp(6*x)+12*exp(5*x)+12*exp(4*x)-exp(3*x)-11*exp(2*x)-6*exp(x)+6)))) \\ G. C. Greubel, Oct 07 2017

Formula

E.g.f.: (1/4!)*(exp(15*x) - 4*exp(8*x) - 6*exp(7*x) - 3*exp(6*x) + 12*exp(5*x) + 12*exp(4*x) - exp(3*x) - 11*exp(2*x) - 6*exp(x) + 6).