A292231 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals five.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Index entries for sequences related to rooted trees

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

Adjacent sequences: A292228 A292229 A292230 * A292232 A292233 A292234

Keyword

nonn

Author

Alois P. Heinz, Sep 12 2017

Status

approved