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A244407 Number of unlabeled rooted trees with 2n nodes and maximal outdegree (branching factor) n. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)