A287890 Number of unrooted labeled 4-cactus graphs on 3n+1 nodes.

1, 3, 630, 756000, 2740537800, 22317642547200, 344030189461358400, 8979238155223784448000, 366881017725878906250000000, 22141857318039212329716940800000, 1887349497873286715447530129178400000, 219275034010568207287452830493455155200000

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-1)*(3*n)!/(2^n*n!). - Andrew Howroyd, Feb 17 2020

Mathematica

Table[(3 n + 1)^(n-1) (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))))/x)); vector(n+1, k, polcoef(p, 3*k-3))} \\ Andrew Howroyd, Feb 17 2020
(Magma) [(3*n+1)^(n-1)*Factorial(3*n)/(2^n*Factorial(n)): n in [0..12]]; // Vincenzo Librandi, Feb 19 2020

Crossrefs

Cf. A034941, A287889, A287891, A287892.

Sequence in context: A140029 A161964 A229688 * A091261 A332163 A230808

Adjacent sequences: A287887 A287888 A287889 * A287891 A287892 A287893

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