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%I #17 Sep 08 2022 08:46:19
%S 1,12,4410,7560000,35626991400,357082280755200,6536573599765809600,
%T 197543239414923257856000,9172025443146972656250000000,
%U 619972004905097945232074342400000,58507834434071888178873434004530400000,7455351156359319047773396236777475276800000
%N Number of rooted labeled 4-cactus graphs on 3n+1 nodes.
%H Andrew Howroyd, <a href="/A287889/b287889.txt">Table of n, a(n) for n = 0..100</a>
%H Maryam Bahrani and Jérémie Lumbroso, <a href="http://arxiv.org/abs/1608.01465">Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition</a>, arXiv:1608.01465 [math.CO], 2016.
%F a(n) = (3*n+1)^n*(3*n)!/(2^n*n!). - _Andrew Howroyd_, Feb 17 2020
%t Table[(3 n + 1)^n (3 n)! / (2^n n!), {n, 0, 15}] (* _Vincenzo Librandi_, Feb 19 2020 *)
%o (PARI) seq(n)={my(p=serlaplace(serreverse(x*exp(-x^3/2 + O(x^(3*n+1)))))); vector(n+1, k, polcoef(p, 3*k-2))} \\ _Andrew Howroyd_, Feb 17 2020
%o (Magma) [(3*n+1)^n*Factorial(3*n)/(2^n*Factorial(n)): n in [0..12]]; // _Vincenzo Librandi_, Feb 19 2020
%Y Cf. A034940, A287890, A287891, A287892.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 21 2017
%E a(0) changed and terms a(7) and beyond from _Andrew Howroyd_, Feb 17 2020
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