A244406 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 10.

1, 2, 6, 17, 50, 143, 416, 1199, 3474, 10049, 29118, 84370, 244718, 710081, 2061842, 5989898, 17411214, 50634907, 147327663, 428858279, 1248914115, 3638554143, 10604615353, 30918735919, 90178253585, 263104102071, 767878267996, 2241762411780, 6546561427512

Offset

11,2

Links

Alois P. Heinz, Table of n, a(n) for n = 11..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, 10$2) -`if`(k=0, 0, b(n-1$2, 9$2)):
seq(a(n), n=11..40);

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, 10, 10] - If[n == 0, 0, b[n - 1, n - 1, 9, 9]]; Table[a[n], {n, 11, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=10 of A244372.

Sequence in context: A244403 A244404 A244405 * A244407 A173993 A270863

Adjacent sequences: A244403 A244404 A244405 * A244407 A244408 A244409

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved