A297204 Number of label-increasing forests with branching bounded by 5.

1, 1, 1, 2, 6, 24, 120, 719, 5017, 39938, 357100, 3542771, 38615127, 458663713, 5896341413, 81562642449, 1207920218823, 19068760619088, 319648589219950, 5670332828427154, 106122789165032548, 2089715042280197113

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..5} (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..5), 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, 5}], 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, A297200, A297201, A297202, A297203.

Sequence in context: A364234 A052398 A047890 * A071088 A177533 A370384

Adjacent sequences: A297201 A297202 A297203 * A297205 A297206 A297207

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2018

Extensions

Corrected and extended by Max Alekseyev, Jul 12 2019

Status

approved