OFFSET
1,3
COMMENTS
Also the number of unordered, leaf-labeled increasing trees on n leaves with maximum node outdegree 3.
LINKS
Johannes Wirtz, Table of n, a(n) for n = 1..1000
Johannes Wirtz, On the enumeration of leaf-labelled increasing trees with arbitrary node-degree, arXiv:2211.03632 [q-bio.PE], 2022.
FORMULA
a(n) = n*(n-1)*((n-2)*a(n-2) + 3*a(n-1))/6 for n >= 3.
a(n+1) ~ 2*Pi*exp(-2/3)*Gamma(5/3)^(-1)*n^(2n+8/3)*2^(-n)*exp^(-2n).
2*Pi*exp(-2/3)*Gamma(5/3)^(-1) = 3.573427548...
MAPLE
a := proc(n) option remember; if n < 2 then return 1 else
a(n-2)*binomial(n, 3) + a(n-1)*binomial(n, 2) fi end:
seq(a(n), n = 1..17);
CROSSREFS
KEYWORD
nonn
AUTHOR
Johannes Wirtz, Oct 29 2022
STATUS
approved