login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297204 Number of label-increasing forests with branching bounded by 5. 7
1, 1, 1, 2, 6, 24, 120, 719, 5017, 39938, 357100, 3542771, 38615127, 458663713, 5896341413, 81562642449, 1207920218823, 19068760619088, 319648589219950, 5670332828427154, 106122789165032548, 2089715042280197113 (list; graph; refs; listen; history; text; internal format)
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: A248838 A052398 A047890 * A071088 A177533 A122417

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 17:09 EST 2022. Contains 358535 sequences. (Running on oeis4.)