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%I #17 Sep 08 2022 08:46:19
%S 1,3,630,756000,2740537800,22317642547200,344030189461358400,
%T 8979238155223784448000,366881017725878906250000000,
%U 22141857318039212329716940800000,1887349497873286715447530129178400000,219275034010568207287452830493455155200000
%N Number of unrooted labeled 4-cactus graphs on 3n+1 nodes.
%H Andrew Howroyd, <a href="/A287890/b287890.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-1)*(3*n)!/(2^n*n!). - _Andrew Howroyd_, Feb 17 2020
%t Table[(3 n + 1)^(n-1) (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))))/x)); vector(n+1, k, polcoef(p, 3*k-3))} \\ _Andrew Howroyd_, Feb 17 2020
%o (Magma) [(3*n+1)^(n-1)*Factorial(3*n)/(2^n*Factorial(n)): n in [0..12]]; // _Vincenzo Librandi_, Feb 19 2020
%Y Cf. A034941, A287889, 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