A244459 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5.

1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 4, 7, 12, 16, 21, 29, 43, 65, 99, 142, 206, 297, 436, 641, 945, 1383, 2029, 2976, 4378, 6432, 9464, 13913, 20495, 30205, 44547, 65670, 96846, 142857, 210941, 311636, 460613, 680848, 1006682, 1488915, 2203324, 3261840, 4830671

Offset

6,7

Links

Alois P. Heinz, Table of n, a(n) for n = 6..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, 5$2) -b(n-1$2, 6$2):
seq(a(n), n=6..55);

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, 5, 5] - b[n - 1, n - 1, 6, 6]; Table[a[n], {n, 6, 55}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=5 of A244454.

Cf. A244534.

Sequence in context: A060824 A334125 A364811 * A064849 A269302 A132189

Adjacent sequences: A244456 A244457 A244458 * A244460 A244461 A244462

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved