A114933 - OEIS

%I #10 Dec 17 2022 08:25:13

%S 0,0,0,32,1094,23055,405475,6575842,102567444,1569195485,23775369725,

%T 358461659952,5391042181294,80974624209115,1215462744452775,

%U 18238484835400862,273628186560143144,4104820038944901945

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

%H G. C. Greubel, <a href="/A114933/b114933.txt">Table of n, a(n) for n = 0..845</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.: (1/4!)*(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).

%t 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 *)

%o (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

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

%K easy,nonn

%O 0,4

%A Goran Kilibarda and _Vladeta Jovovic_, Jan 08 2006