A244534 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5.

1, 0, 0, 0, 0, 5, 11, 12, 13, 14, 50, 136, 289, 477, 703, 1255, 2611, 5489, 10902, 19712, 35455, 66651, 130014, 254737, 488041, 920461, 1741642, 3338360, 6453073, 12425997, 23780944, 45451155, 87224392, 168253246, 324863578, 625728091, 1202953325, 2314485753

Offset: 6

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000

Crossrefs

Column k=5 of A244530.

Cf. A244459.

Programs

Maple

b:= proc(n, t, k) option remember; `if`(n=0,
      `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
       b(n-j, max(0, t-1), k), j=1..n)))
    end:
a:= n-> b(n-1, 5$2) -b(n-1, 6$2):
seq(a(n), n=6..50);

Mathematica

b[n_, t_, k_] := b[n, t, k] = If[n == 0,
     If[MemberQ[{0, k}, t], 1, 0], If[t > n, 0, Sum[b[j-1, k, k]*
     b[n-j, Max[0, t-1], k], {j, n}]]];
a[n_] := b[n-1, 5, 5] - b[n-1, 6, 6];
Table[a[n], {n, 6, 50}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)