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A244405
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 9.
2
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
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
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved