A244461 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 7.

1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 4, 7, 12, 16, 21, 25, 30, 38, 52, 74, 108, 151, 206, 271, 356, 468, 629, 855, 1180, 1620, 2212, 2991, 4030, 5420, 7320, 9922, 13508, 18396, 25049, 34032, 46194, 62653, 85051, 115548, 157168, 213852, 291046, 395990

Offset

8,9

Links

Alois P. Heinz, Table of n, a(n) for n = 8..900

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
      1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
      b(n-i*j, i-1, max(0, t-j), k), j=0..n/i)))
    end:
a:= n-> b(n-1$2, 7$2) -b(n-1$2, 8$2):
seq(a(n), n=8..65);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 7, 7] - b[n - 1, n - 1, 8, 8]; Table[a[n], {n, 8, 65}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=7 of A244454.

Cf. A244536.

Sequence in context: A202709 A279611 A008767 * A366811 A343925 A105255

Adjacent sequences: A244458 A244459 A244460 * A244462 A244463 A244464

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved