A292210 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than four.

0, 1, 1, 2, 5, 11, 30, 80, 228, 656, 1945, 5835, 17808, 54881, 170951, 536726, 1697774, 5403629, 17295686, 55630538, 179726346, 582942079, 1897565974, 6196973039, 20297954197, 66666192488, 219505550167, 724415274090, 2395838962114, 7939424272536

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, 4)))
    end:
seq(a(n), n=0..35);

Crossrefs

Column k=4 of A292085.

Sequence in context: A121134 A144959 A131347 * A079225 A139466 A291139

Adjacent sequences: A292207 A292208 A292209 * A292211 A292212 A292213

Keyword

nonn

Author

Alois P. Heinz, Sep 11 2017

Status

approved