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A244406
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 10.
2
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
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
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved