cp's OEIS Frontend

A124501 Number of 1-2-3-4-5-6 trees with n edges and with thinning limbs. A 1-2-3-4-5-6 tree is an ordered tree with vertices of outdegree at most 6. A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.

%I A124501 #6 Oct 06 2013 13:58:24
%S A124501 1,1,2,4,10,25,68,186,522,1479,4246,12289,35872,105411,311662,926270,
%T A124501 2765778,8292296,24953437,75338686,228140842,692733127,2108652750,
%U A124501 6433255041,19668210742,60247367313,184879648441,568281131800
%N A124501 Number of 1-2-3-4-5-6 trees with n edges and with thinning limbs. A 1-2-3-4-5-6 tree is an ordered tree with vertices of outdegree at most 6. A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.
%C A124501 The sequences corresponding to k=2 (A090344), k=3 (A124497), k=4 (A124499), k=5 (A124500), k=6 (this A124501), etc. approach sequence A124344, corresponding to ordered trees with thinning limbs.
%F A124501 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).
%o A124501 (PARI) {a(n)=local(k=6,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_
%Y A124501 Cf. A090344, A124497, A124499, A124500, A124344.
%K A124501 nonn
%O A124501 0,3
%A A124501 _Emeric Deutsch_ and _Louis Shapiro_, Nov 06 2006