

A124500


Number of 12345 trees with n edges and with thinning limbs. A 12345 tree is an ordered tree with vertices of outdegree at most 5. A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.


3



1, 1, 2, 4, 10, 25, 67, 180, 495, 1375, 3871, 10993, 31493, 90843, 263686, 769466, 2256135, 6643082, 19634705, 58232350, 173242381, 516860717, 1546035258, 4635543843, 13929569399, 41943013047, 126532961332, 382396277940
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

The sequences corresponding to k=2 (A090344), k=3 (A124497), k=4 (A124499), k=5 (this A124500), etc. approach sequence A124344, corresponding to ordered trees with thinning limbs.


LINKS

Table of n, a(n) for n=0..27.


FORMULA

In general, if M[k](z) is the g.f. of the 12...k trees with thinning limbs and C[k](z)=1+z*{C[k](z)}^k is the g.f. of the kary trees, then M[k](z)=M[k1](z)*C[k](M[k1]^(k1)*z^k), M[1](z)=1/(1z).


PROG

(PARI) {a(n)=local(k=5, M=1+x*O(x^n)); for(i=1, k, M=M*sum(j=0, n, binomial(i*j, j)/((i1)*j+1)*(x^i*M^(i1))^j)); polcoeff(M, n)} \\ Paul D. Hanna


CROSSREFS

Cf. A090344, A124497, A124499, A124501, A124344.
Sequence in context: A189912 A268321 A195981 * A220872 A317876 A124501
Adjacent sequences: A124497 A124498 A124499 * A124501 A124502 A124503


KEYWORD

nonn


AUTHOR

Emeric Deutsch and Louis Shapiro, Nov 06 2006


STATUS

approved



