A292749 Number of 6-good trees with n nodes.

1, 1, 2, 6, 24, 120, 721, 5075, 41146, 379764, 3955413, 46147101, 598757159, 8574963397, 134469746411, 2290379988897, 42043096791696, 825840722368662, 17251010028434182, 381214917773329640, 8873155199416851343, 216770612918353773279, 5542237907509303118118

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

John Engbers, David Galvin, Clifford Smyth, Restricted Stirling and Lah numbers and their inverses, arXiv:1610.05803 [math.CO], 2016.

Formula

a(n) = (-1)^(n-1) * n! * [x^n]g(x) where g(x) is the series reversion of 1+x+x^2/2!+x^3/3!+x^4/4+x^5/5!+x^6/6! [see p. 21 of Engbers, Galvin, and Smyth]. - Sean A. Irvine, Aug 23 2019

Prog

(PARI) Vec(serlaplace(serreverse(-sum(k=1, 6, (-1)^k*x^k/k!) + O(x^30)))) \\ Andrew Howroyd, Dec 24 2025

Crossrefs

Cf. A292748 (4-good trees).

Sequence in context: A265086 A114790 A352430 * A351984 A365977 A079854

Adjacent sequences: A292746 A292747 A292748 * A292750 A292751 A292752

Keyword

nonn

Author

N. J. A. Sloane, Sep 22 2017

Extensions

More terms from Sean A. Irvine, Aug 23 2019

Status

approved