A287889 Number of rooted labeled 4-cactus graphs on 3n+1 nodes.

1, 12, 4410, 7560000, 35626991400, 357082280755200, 6536573599765809600, 197543239414923257856000, 9172025443146972656250000000, 619972004905097945232074342400000, 58507834434071888178873434004530400000, 7455351156359319047773396236777475276800000

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

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

Cf. A034940, A287890, A287891, A287892.

Sequence in context: A096732 A127233 A169657 * A288967 A361106 A009094

Adjacent sequences: A287886 A287887 A287888 * A287890 A287891 A287892

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