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A127525 Number of ordered rooted trees where each subtree from given node has the same number of nodes. 5
1, 1, 2, 3, 5, 6, 12, 13, 24, 33, 60, 61, 142, 143, 289, 447, 699, 700, 1558, 1559, 3518, 5375, 8977, 8978, 17179, 20305, 40471, 54808, 98182, 98183, 242068, 242069, 477002, 695051, 1183654, 1510612, 2629806, 2629807, 5057173, 7928654, 12366025, 12366026 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..5590

FORMULA

a(1) = 1; a(n+1) = Sum_{d|n} a(n/d)^d.

L.g.f.: -log(Product_{n>=1} (1 - a(n)*x^n)^(1/n)) = Sum_{n>=1} a(n+1)*x^n/n. - Ilya Gutkovskiy, Apr 29 2019

EXAMPLE

The tree shown below left counts, because the left subtree has 3 nodes and so does the right subtree and a similar condition holds for the subtrees. The tree shown on the right is not counted, because the left subtree has 3 nodes, while the right subtree has 4.

O..........O...O...O

|..........|....\./.

O...O...O..O.....O..

.\...\./....\....|..

.O...O......O...O..

..\./........\./...

...O..........O....

MAPLE

a:= proc(n) option remember; `if`(n<2, n, add(

      a((n-1)/d)^d, d=numtheory[divisors](n-1)))

    end:

seq(a(n), n=1..45);  # Alois P. Heinz, Sep 08 2018

MATHEMATICA

a[1] = 1;

a[n_] := a[n] = Sum[a[(n-1)/d]^d, {d, Divisors[n-1]}];

Array[a, 45] (* Jean-Fran├žois Alcover, Oct 28 2020 *)

CROSSREFS

Cf. A000108, A127524, A007059.

Sequence in context: A174100 A114339 A339308 * A179333 A128958 A007435

Adjacent sequences:  A127522 A127523 A127524 * A127526 A127527 A127528

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jan 17 2007

STATUS

approved

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Last modified January 19 22:04 EST 2022. Contains 350466 sequences. (Running on oeis4.)