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A244401
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 5.
2
1, 2, 6, 17, 50, 142, 409, 1169, 3356, 9617, 27601, 79210, 227527, 653793, 1879867, 5407806, 15564968, 44820889, 129127761, 372177974, 1073169150, 3095721985, 8933568154, 25789862435, 74477871565, 215155604291, 621754458752, 1797297119000, 5196966140656
OFFSET
6,2
LINKS
FORMULA
a(n) = A036721(n) - A036718(n).
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, 5$2) -`if`(k=0, 0, b(n-1$2, 4$2)):
seq(a(n), n=6..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, 5, 5] - If[n == 0, 0, b[n-1, n-1, 4, 4]]; Table[a[n], {n, 6, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
Column k=5 of A244372.
Sequence in context: A336742 A148445 A148446 * A244402 A244403 A244404
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved