A244403 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 7.

1, 2, 6, 17, 50, 143, 416, 1198, 3467, 10019, 29001, 83945, 243228, 705012, 2044935, 5934425, 17231410, 50058023, 145491836, 423056364, 1230683672, 3581556220, 10427172296, 30368394833, 88476965536, 257860132679, 751756288476, 2192311994070, 6395199688864

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Formula

a(n) = A182378(n) - A036722(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, 7$2) -`if`(k=0, 0, b(n-1$2, 6$2)):
seq(a(n), n=8..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, 7, 7] - If[n == 0, 0, b[n - 1, n - 1, 6, 6]]; Table[a[n], {n, 8, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=7 of A244372.

Cf. A036722, A182378.

Sequence in context: A148446 A244401 A244402 * A244404 A244405 A244406

Adjacent sequences: A244400 A244401 A244402 * A244404 A244405 A244406

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved