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A292211
Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than five.
2
0, 1, 1, 2, 5, 12, 32, 87, 251, 733, 2201, 6696, 20705, 64681, 204183, 649738, 2082939, 6719063, 21796084, 71052001, 232645645, 764768959, 2523033061, 8350789334, 27721841968, 92277902858, 307935654094, 1029970333229, 3452371784462, 11595031966743
OFFSET
0,4
MAPLE
b:= proc(n, i, v) 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)+j-1, j)*
b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
end:
a:= proc(n) option remember; `if`(n<2, n,
add(b(n, n+1-j, j), j=2..min(n, 5)))
end:
seq(a(n), n=0..35);
CROSSREFS
Column k=5 of A292085.
Sequence in context: A335456 A345200 A173611 * A293348 A188287 A363240
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 11 2017
STATUS
approved