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

0,3

Links

Table of n, a(n) for n=0..20.

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

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

Crossrefs

Cf. A011800.

Sequence in context: A308204 A307724 A029851 * A207557 A235129 A222033

Adjacent sequences: A201717 A201718 A201719 * A201721 A201722 A201723

Keyword

nonn

Author

Geoffrey Critzer, Dec 04 2011

Status

approved