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A127524 Number of unordered rooted trees where each subtree from given node has the same number of nodes. 14
1, 1, 2, 3, 5, 6, 11, 12, 20, 25, 42, 43, 81, 82, 150, 192, 287, 288, 563, 564, 982, 1277, 2182, 2183, 3658, 3785, 7108, 8659, 13101, 13102, 27827, 27828, 47768, 61025, 102355, 105689, 170882, 170883, 329651, 421547, 606283, 606284, 1193038, 1193039, 2158117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(1) = 1; a(n+1) = Sum_{d|n} C(a(n/d) + d-1, d).

EXAMPLE

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

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

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

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

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

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

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

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

MAPLE

with(numtheory):

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

      add(binomial(a((n-1)/d)+d-1, d), d=divisors(n-1)))

    end:

seq(a(n), n=1..50);  # Alois P. Heinz, May 16 2013

MATHEMATICA

a[1] = 1; a[n_] := a[n] = DivisorSum[n-1, Binomial[a[(n-1)/#]+#-1, #]&]; Table[a[n], {n, 1, 50}] (* Jean-Fran├žois Alcover, Feb 25 2017 *)

CROSSREFS

Cf. A000081, A127525.

Sequence in context: A332275 A318689 A083710 * A117086 A081026 A137808

Adjacent sequences:  A127521 A127522 A127523 * A127525 A127526 A127527

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jan 17 2007

STATUS

approved

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Last modified April 10 20:32 EDT 2021. Contains 342856 sequences. (Running on oeis4.)