A114935 - OEIS

%I #10 Dec 17 2022 08:25:51

%S 0,1,6,44,332,2476,18136,130824,933372,6610676,46603616,327603904,

%T 2298933412,16115938476,112906938696,790735321784,5536710117452,

%U 38763269947876,271368229299376,1899679393564464,13298164198917492

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

%H G. C. Greubel, <a href="/A114935/b114935.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) +5*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] + 5*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], Vec(serlaplace((1/3!)*(exp(7*x) -3*exp(4*x) +5*exp(3*x) -3*exp(2*x) +2*exp(x) - 2)))) \\ _G. C. Greubel_, Oct 07 2017

%Y Cf. A002501, A002502, A093732, A093732, A093733, A114934, A114936, A114937.

%K easy,nonn

%O 0,3

%A Goran Kilibarda and _Vladeta Jovovic_, Jan 08 2006