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A292214 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than eight. 2

%I

%S 0,1,1,2,5,12,33,90,261,765,2309,7058,21932,68843,218378,698268,

%T 2249370,7291072,23766308,77850244,256141505,846090860,2804864997,

%U 9328658392,31118365152,104086821258,349029100890,1173087112579,3951183698640,13334782347941

%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than eight.

%H Alois P. Heinz, <a href="/A292214/b292214.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%p b:= proc(n, i, v) option remember; `if`(n=0,

%p `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,

%p `if`(v=n, 1, add(binomial(a(i)+j-1, j)*

%p b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))

%p end:

%p a:= proc(n) option remember; `if`(n<2, n,

%p add(b(n, n+1-j, j), j=2..min(n, 8)))

%p end:

%p seq(a(n), n=0..35);

%Y Column k=8 of A292085.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Sep 11 2017

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Last modified May 25 00:59 EDT 2019. Contains 323534 sequences. (Running on oeis4.)