A297200 Number of label-increasing forests with branching bounded by 4.

1, 1, 1, 2, 6, 24, 119, 703, 4819, 37596, 328871, 3187627, 33907426, 392693219, 4918535904, 66246158633, 954739609059, 14660169150206, 238933675330056, 4119463404086442, 74907534899129351, 1432718565376182929

Offset

0,4

Comments

See Riordan 1978 or 1979 for precise definition.

Links

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

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..4} (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..4), 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, 4}], x] + O[x]^m // Normal, {m}];
CoefficientList[F[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Oct 26 2019 *)

Crossrefs

Cf. A297196, A297197, A297198, A297201, A297202, A297203, A297204.

Sequence in context: A256208 A264432 A094198 * A071077 A202213 A202216

Adjacent sequences: A297197 A297198 A297199 * A297201 A297202 A297203

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2018

Extensions

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

Status

approved