A292211 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than five.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to rooted trees

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

Adjacent sequences: A292208 A292209 A292210 * A292212 A292213 A292214

Keyword

nonn

Author

Alois P. Heinz, Sep 11 2017

Status

approved