OFFSET
0,4
COMMENTS
See Riordan 1978 or 1979 for precise definition.
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 10 2018
EXTENSIONS
Edited and more terms added by Max Alekseyev, Jul 12 2019
STATUS
approved