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A244410 Number of unlabeled rooted trees with 2n+1 nodes and maximal outdegree (branching factor) n. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified April 4 19:22 EDT 2020. Contains 333229 sequences. (Running on oeis4.)