A292214 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than eight.

0, 1, 1, 2, 5, 12, 33, 90, 261, 765, 2309, 7058, 21932, 68843, 218378, 698268, 2249370, 7291072, 23766308, 77850244, 256141505, 846090860, 2804864997, 9328658392, 31118365152, 104086821258, 349029100890, 1173087112579, 3951183698640, 13334782347941

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, 8)))
    end:
seq(a(n), n=0..35);

Crossrefs

Column k=8 of A292085.

Sequence in context: A212823 A292213 A032124 * A292215 A292216 A000669

Adjacent sequences: A292211 A292212 A292213 * A292215 A292216 A292217

Keyword

nonn

Author

Alois P. Heinz, Sep 11 2017

Status

approved