A244533 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.

1, 0, 0, 0, 4, 9, 10, 11, 34, 91, 196, 330, 636, 1377, 2976, 6061, 12199, 25186, 52767, 109066, 224964, 467605, 979056, 2042847, 4244986, 8844130, 18527956, 38878929, 81460220, 170576593, 357894472, 752544917, 1583579674, 3332453026, 7016669752, 14790212086

Offset: 5

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000
• Vaclav Kotesovec, Recurrence (of order 11)

Crossrefs

Column k=4 of A244530.

Cf. A244458.

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, 4$2) -b(n-1, 5$2):
seq(a(n), n=5..45);

Mathematica

b[n_, t_, k_] := b[n, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[t > n, 0, Sum[b[j - 1, k, k]*b[n - j, Max[0, t - 1], k], {j, 1, n}]]]; T[n_, k_] := b[n - 1, k, k] - If[n == 1 && k == 0, 0, b[n - 1, k + 1, k + 1]]; a[n_] := b[n - 1, 4, 4] - b[n - 1, 5, 5]; Table[a[n], {n, 5, 45}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Formula

a(n) ~ c * d^n / (sqrt(Pi) * n^(3/2)), where d = 2.18452974131524781307797151868229485574758... is the root of the equation -229 - 36*d + 2*d^2 - 32*d^3 + 19*d^4 + 4*d^5 = 0, and c = 0.181069926661856899940163775713243367029404419526724... . - Vaclav Kotesovec, Jul 02 2014