A244407 Number of unlabeled rooted trees with 2n nodes and maximal outdegree (branching factor) n.

1, 2, 6, 17, 50, 143, 416, 1199, 3474, 10049, 29119, 84377, 244748, 710199, 2062274, 5991418, 17416401, 50652248, 147384676, 429043390, 1249508947, 3640449679, 10610613552, 30937605076, 90237313083, 263288153074, 768449666117, 2243530461067, 6552016136667

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Formula

a(n) = A244372(2n,n).

a(n) ~ c * d^n / sqrt(n), where d = 2.955765285651994974714817524... is the Otter's rooted tree constant (see A051491), and c = 0.9495793... . - Vaclav Kotesovec, Jul 11 2014

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
    end:
a:= n-> b(2*n-1$2, n$2)-b(2*n-1$2, n-1$2):
seq(a(n), n=1..30);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]* b[n - i*j, i - 1, t - j, k], {j, 0, Min[t, n/i]}]] // FullSimplify] ; a[n_] := b[2*n - 1, 2 n - 1, n, n] - b[2*n - 1, 2 n - 1, n - 1, n - 1]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Cf. A244372, A244410, A051491, A299039.

Sequence in context: A244404 A244405 A244406 * A173993 A270863 A027914

Adjacent sequences: A244404 A244405 A244406 * A244408 A244409 A244410

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved