A244410 Number of unlabeled rooted trees with 2n+1 nodes and maximal outdegree (branching factor) n.

1, 1, 5, 16, 49, 142, 415, 1198, 3473, 10048, 29118, 84376, 244747, 710198, 2062273, 5991417, 17416400, 50652247, 147384675, 429043389, 1249508946, 3640449678, 10610613551, 30937605075, 90237313082, 263288153073, 768449666116, 2243530461066, 6552016136666

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Formula

a(n) = A244372(2n+1,n).

a(n) ~ c * d^n / sqrt(n), where d = 2.955765285651994974714817524... is the Otter's rooted tree constant (see A051491), and c = 2.806733... . - 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-> `if`(n=0, 1, b(2*n$2, n$2)-b(2*n$2, n-1$2)):
seq(a(n), n=0..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_] := If[n == 0, 1, b[2*n, 2 n, n, n] - b[2*n, 2 n, n - 1, n - 1]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Cf. A244372, A244407, A051491.

Sequence in context: A055144 A171426 A180129 * A052909 A037536 A192904

Adjacent sequences: A244407 A244408 A244409 * A244411 A244412 A244413

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved