A303259 Number of ordered rooted trees with n non-root nodes such that the maximal outdegree equals ceiling(n/2).

1, 1, 1, 3, 8, 15, 53, 84, 326, 495, 1997, 3003, 12370, 18564, 77513, 116280, 490306, 735471, 3124541, 4686825, 20030000, 30045015, 129024469, 193536720, 834451788, 1251677700, 5414950283, 8122425444, 35240152706, 52860229080, 229911617041, 344867425584

Offset: 0

Author

Alois P. Heinz, Apr 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2417

Crossrefs

Bisections give: A291662 (even part), A005809 (odd part).

Cf. A203717.

Programs

Maple

b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
      add(b(u-j, o+j-1, k), j=1..min(1, u))+
      add(b(u+j-1, o-j, k), j=1..min(k, o)))
    end:
a:= n-> `if`(n=0, 1, (j-> b(0, n, j)-b(0, n, j-1))(ceil(n/2))):
seq(a(n), n=0..35);

Mathematica

b[u_, o_, k_] := b[u, o, k] = If[u + o == 0, 1,
     Sum[b[u - j, o + j - 1, k], {j, 1, Min[1, u]}] +
     Sum[b[u + j - 1, o - j, k], {j, 1, Min[k, o]}]];
a[n_] := If[n == 0, 1, With[{j = Ceiling[n/2]}, b[0, n, j]-b[0, n, j-1]]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 19 2022, after Alois P. Heinz *)

Formula

a(n) = A203717(n,ceiling(n/2)).