A318804 - OEIS

%I #7 Sep 04 2018 17:03:30

%S 0,1,1,2,4,9,20,48,115,286,719,1842,4765,12484,32968,87798,235346,

%T 634752,1720897,4687949,12824195,35216118,97039045,268237121,

%U 743594937,2066803841,5758576675,16080698759,44998355630,126161517745,354354779794,996963790045,2809334906744,7928088014833,22404525682610

%N Number of rooted trees with n nodes such that no more than ten subtrees of the same size extend from the same node.

%C This differs from A318857 first at n=34.

%H Alois P. Heinz, <a href="/A318804/b318804.txt">Table of n, a(n) for n = 0..2136</a>

%p g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

%p       binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(10, n/i))))

%p     end:

%p a:= n-> g((n-1)$2):

%p seq(a(n), n=0..40);

%Y Column k=10 of A318753.

%Y Cf. A318857.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Sep 03 2018