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A287889
Number of rooted labeled 4-cactus graphs on 3n+1 nodes.
4
1, 12, 4410, 7560000, 35626991400, 357082280755200, 6536573599765809600, 197543239414923257856000, 9172025443146972656250000000, 619972004905097945232074342400000, 58507834434071888178873434004530400000, 7455351156359319047773396236777475276800000
OFFSET
0,2
LINKS
Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.
FORMULA
a(n) = (3*n+1)^n*(3*n)!/(2^n*n!). - Andrew Howroyd, Feb 17 2020
MATHEMATICA
Table[(3 n + 1)^n (3 n)! / (2^n n!), {n, 0, 15}] (* Vincenzo Librandi, Feb 19 2020 *)
PROG
(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
(Magma) [(3*n+1)^n*Factorial(3*n)/(2^n*Factorial(n)): n in [0..12]]; // Vincenzo Librandi, Feb 19 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 21 2017
EXTENSIONS
a(0) changed and terms a(7) and beyond from Andrew Howroyd, Feb 17 2020
STATUS
approved