A124500 Number of 1-2-3-4-5 trees with n edges and with thinning limbs. A 1-2-3-4-5 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.

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

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 1-2-...-k trees with thinning limbs and C[k](z)=1+z*{C[k](z)}^k is the g.f. of the k-ary trees, then M[k](z)=M[k-1](z)*C[k](M[k-1]^(k-1)*z^k), M[1](z)=1/(1-z).

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)/((i-1)*j+1)*(x^i*M^(i-1))^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