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A244456 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 2. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 06 2015, after Maple *)

CROSSREFS

Column k=2 of A244454.

Cf. A244531, A246403.

Sequence in context: A299099 A248574 A136336 * A232394 A115178 A331934

Adjacent sequences:  A244453 A244454 A244455 * A244457 A244458 A244459

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 29 2014

STATUS

approved

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Last modified August 6 15:33 EDT 2020. Contains 336251 sequences. (Running on oeis4.)