A201720 The total number of components in (A011800) of all labeled forests on n nodes whose components are all paths.

0, 1, 3, 12, 64, 420, 3246, 28798, 288072, 3205044, 39234340, 523821936, 7572221328, 117792884872, 1961516974704, 34807390821960, 655594811020096, 13060711726818768, 274358217793164912, 6060159633360214144, 140404595387426964480

Offset: 0

Author

Geoffrey Critzer, Dec 04 2011

Keywords

• nonn

Crossrefs

Cf. A011800.

Programs

Maple

A201720 := proc(n)
    g := (2*x-x^2)*exp((2*x-x^2)/(2-2*x))/(2-2*x) ;
    coeftayl(g,x=0,n) ;
    %*n! ;
end proc:
seq(A201720(n),n=0..30) ; # R. J. Mathar, Jun 27 2022

Mathematica

D[Range[0, 20]! CoefficientList[ Series[Exp[y (2 x - x^2)/(2 - 2 x)], {x, 0, 20}], x], y] /. y -> 1

Formula

E.g.f.: x*(2-x)*exp[x*(2-x)/(2-2x)]/(2-2x). - R. J. Mathar, Jun 27 2022

D-finite with recurrence 6*(n+1)*a(n) +2*(-6*n^2-19*n+35)*a(n-1) +2*(3*n^3+26*n^2-102*n+75)*a(n-2) -(n-2)*(29*n^2-102*n+85)*a(n-3) +(13*n-15)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jun 27 2022