A244404 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 8.

1, 2, 6, 17, 50, 143, 416, 1199, 3473, 10042, 29089, 84259, 244316, 708679, 2057087, 5974077, 17359390, 50467157, 146789962, 427148444, 1243513350, 3621591235, 10551595959, 30753712080, 89666493709, 261522175986, 763002239120, 2226771020793, 6500575182332

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..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, 8$2) -`if`(k=0, 0, b(n-1$2, 7$2)):
seq(a(n), n=9..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, 8, 8] - If[n == 0, 0, b[n - 1, n - 1, 7, 7]]; Table[a[n], {n, 9, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=8 of A244372.

Sequence in context: A244401 A244402 A244403 * A244405 A244406 A244407

Adjacent sequences: A244401 A244402 A244403 * A244405 A244406 A244407

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved