A244405 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 9.

1, 2, 6, 17, 50, 143, 416, 1199, 3474, 10048, 29112, 84347, 244630, 709767, 2060754, 5986231, 17399060, 50595235, 147199567, 428448576, 1247613511, 3634451971, 10591746511, 30878554201, 90053295475, 262716880036, 766682072349, 2238077375703, 6535237181868

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..750

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
    end:
a:= n-> b(n-1$2, 9$2) -`if`(k=0, 0, b(n-1$2, 8$2)):
seq(a(n), n=10..45);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]* b[n - i*j, i - 1, t - j, k], {j, 0, Min[t, n/i]}]] // FullSimplify] ; a[n_] := b[n - 1, n - 1, 9, 9] - If[n == 0, 0, b[n - 1, n - 1, 8, 8]]; Table[a[n], {n, 10, 45}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=9 of A244372.

Sequence in context: A244402 A244403 A244404 * A244406 A244407 A173993

Adjacent sequences: A244402 A244403 A244404 * A244406 A244407 A244408

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved