A297196 Number of label-increasing forests with branching bounded by 3.

1, 1, 1, 2, 6, 23, 108, 601, 3863, 28159, 229524, 2068498, 20422119, 219201032, 2541402277, 31651201409, 421417326357, 5973390936116, 89807344973286, 1427447458217437, 23916152814768626, 421268372668968823

Offset

0,4

Comments

See Riordan 1978 or 1979 for precise definition.

Links

Table of n, a(n) for n=0..21.

Letong Hong and Rupert Li, Length-Four Pattern Avoidance in Inversion Sequences, arXiv:2112.15081 [math.CO], 2021.

John Riordan, Forests of label-increasing trees, annotated scanned copy of 1978 pre-publication version.

John Riordan, Forests of label-increasing trees, J. Graph Theory, 3 (1979), 127-133.

Formula

E.g.f. F(x) satisfies the ODE: F'(x) = Sum_{j=0..3} (F(x)-1)^j/j! with F(0)=1. - Max Alekseyev, Jul 12 2019

Maple

Order := 25; F := rhs( dsolve( { diff(y(x), x) = sum((y(x)-1)^j/j!, j=0..3), y(0)=1 }, y(x), type=series ) ); seq( coeff(F, x, n)*n!, n=0..24 ); # Max Alekseyev, Jul 12 2019

Mathematica

m = 22; F[_] = 0;
Do[F[x_] = 1 + Integrate[Sum[(F[x] - 1)^j/j!, {j, 0, 3}], x] + O[x]^m // Normal, {m}];
CoefficientList[F[x], x]*Range[0, m-1]! (* Jean-François Alcover, Oct 26 2019 *)

Crossrefs

Cf. A297197, A297198, A297200, A297201, A297202, A297203, A297204.

Sequence in context: A101053 A155857 A071076 * A112501 A093345 A289681

Adjacent sequences: A297193 A297194 A297195 * A297197 A297198 A297199

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2018

Extensions

Edited and more terms added by Max Alekseyev, Jul 12 2019

Status

approved