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A292231
Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals five.
2
1, 2, 7, 23, 77, 256, 861, 2897, 9800, 33232, 113012, 385165, 1315434, 4500398, 15421463, 52919299, 181826880, 625467087, 2153816295, 7423887771, 25611710370, 88430103927, 305555059139, 1056532822348, 3655607694207, 12656112780583, 43841784746311
OFFSET
5,2
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, 5)-A(n, 4):
seq(a(n), n=5..35);
CROSSREFS
Column k=5 of A292086.
Sequence in context: A052924 A067324 A047062 * A292232 A292233 A292234
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 12 2017
STATUS
approved