A244456 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 2.

1, 0, 1, 2, 4, 7, 15, 28, 56, 110, 220, 436, 878, 1762, 3560, 7205, 14650, 29838, 60991, 124938, 256628, 528238, 1089834, 2252860, 4666304, 9682422, 20125777, 41900433, 87369029, 182441944, 381499040, 798782945, 1674575394, 3514733683, 7385298837, 15534856067

Offset

3,4

Links

Alois P. Heinz, Table of n, a(n) for n = 3..900

Formula

a(n) ~ c * d^n / n^(3/2), where d = A246403 = 2.18946198566085056388702757711..., c = 0.4213018528699249210965028... (constants are same as for A001679). - Vaclav Kotesovec, Jul 02 2014

Example

a(5) = 1:
      o
     / \
    o   o
   / \
  o   o

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, 2$2) -b(n-1$2, 3$2):
seq(a(n), n=3..40);

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}]]]; a[n_] := b[n - 1, n - 1, 2, 2] - b[n - 1, n - 1, 3, 3] // FullSimplify; Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=2 of A244454.

Cf. A244531, A246403.

Sequence in context: A299099 A248574 A136336 * A232394 A356626 A115178

Adjacent sequences: A244453 A244454 A244455 * A244457 A244458 A244459

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved