The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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-François 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)