A292748 Number of 4-good trees with n nodes.

1, 1, 2, 6, 25, 140, 1015, 9065, 95095, 1131900, 14964950, 217091875, 3430276850, 58734600925, 1084950741875, 21527855724375, 456878274102250, 10327751636452250, 247707850627612375, 6281906665784750000, 167928158962254315625, 4719079778905601484375

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.

Sean A. Irvine, Java program (github)

Formula

Coefficients of (x-1) in series reversion of 1+x+x^2/2!+x^3/3!+x^4/4! multiplied by (-1)^(n+1)*n!. - Benedict W. J. Irwin, Aug 16 2019

E.g.f.: A'(x) where A(x) is the series reversion of x - x^2/2 + x^3/6 - x^4/24. - Andrew Howroyd, Aug 24 2019

Mathematica

m = 23;
egf = D[InverseSeries[x - x^2/2 + x^3/6 - x^4/24 + O[x]^m], x];
CoefficientList[egf, x] Range[0, m - 2]! (* Jean-François Alcover, Sep 25 2019 *)

Prog

(PARI) Vec(serlaplace(serreverse(-sum(k=1, 4, (-1)^k*x^k/k!) + O(x^30)))) \\ Andrew Howroyd, Aug 24 2019

Crossrefs

Cf. A292749 (6-good trees).

Sequence in context: A135881 A007815 A195259 * A178087 A109286 A009466

Adjacent sequences: A292745 A292746 A292747 * A292749 A292750 A292751

Keyword

nonn

Author

N. J. A. Sloane, Sep 22 2017

Extensions

More terms from Sean A. Irvine, Aug 23 2019

Status

approved