A244402 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 6.
1, 2, 6, 17, 50, 143, 415, 1192, 3444, 9931, 28687, 82857, 239563, 692878, 2005381, 5806915, 16824277, 48767953, 141430699, 410341703, 1191064873, 3458607705, 10046993035, 29196507434, 84874753458, 246814998803, 717965190047, 2089140528083, 6080768466919
Offset: 7
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 7..1000
Programs
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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, 6$2) -`if`(k=0, 0, b(n-1$2, 5$2)): seq(a(n), n=7..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, 6, 6] - If[n == 0, 0, b[n - 1, n - 1, 5, 5]]; Table[a[n], {n, 7, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)