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A292229
Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals three.
2
1, 2, 6, 17, 47, 133, 380, 1096, 3186, 9351, 27618, 82168, 245882, 740003, 2238186, 6801375, 20754977, 63583715, 195486605, 603003882, 1865692570, 5788676649, 18007192835, 56151236196, 175486946089, 549586009252, 1724530420457, 5421195811358, 17070958403725
OFFSET
3,2
EXAMPLE
: a(5) = 6:
: o o o o o o
: / \ / \ /|\ / \ /|\ / | \
: o N o N o N N o o o N N o o N
: / \ /|\ / \ /|\ ( ) /|\ ( ) ( )
: o N o N N o N N N N N N N N N N N N N
: /|\ ( ) ( )
: N N N N N N N
:
MAPLE
b:= proc(n, i, v, k) option remember; `if`(n=0,
`if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
`if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
end:
A:= proc(n, k) option remember; `if`(n<2, n,
add(b(n, n+1-j, j, k), j=2..min(n, k)))
end:
a:= n-> A(n, 3)-A(n, 2):
seq(a(n), n=3..35);
CROSSREFS
Column k=3 of A292086.
Sequence in context: A356934 A200379 A032638 * A090039 A299166 A136776
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 12 2017
STATUS
approved