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A292233
Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals seven.
2
1, 2, 7, 23, 78, 262, 892, 3034, 10379, 35581, 122338, 421498, 1455216, 5032559, 17431384, 60460263, 209967105, 729996715, 2540602259, 8850326207, 30857134567, 107670278671, 375970664930, 1313731592633, 4593388008873, 16069958896737, 56251584472388
OFFSET
7,2
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, 7)-A(n, 6):
seq(a(n), n=7..35);
CROSSREFS
Column k=7 of A292086.
Sequence in context: A047062 A292231 A292232 * A292234 A292235 A292236
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 12 2017
STATUS
approved