A299098 Number of rooted identity trees with 2n nodes.

0, 1, 2, 6, 25, 113, 548, 2770, 14426, 76851, 416848, 2294224, 12780394, 71924647, 408310668, 2335443077, 13446130438, 77863375126, 453203435319, 2649957419351, 15558520126830, 91687179000949, 542139459641933, 3215484006733932, 19125017153077911

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1253

Formula

a(n) = A004111(2*n).

Example

a(3) = 6:
   o     o       o       o       o         o
   |     |       |      / \     / \       / \
   o     o       o     o   o   o   o     o   o
   |     |      / \    |       |   |    / \
   o     o     o   o   o       o   o   o   o
   |    / \    |       |       |       |
   o   o   o   o       o       o       o
   |   |       |       |
   o   o       o       o
   |
   o

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(
      b(d)*d*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
    end:
a:= n-> b(2*n):
seq(a(n), n=0..30);

Mathematica

b[n_] := b[n] = If[n<2, n, Sum[b[n-k]*Sum[b[d]*d*(-1)^(k/d + 1), {d, Divisors[k]}], {k, 1, n-1}]/(n-1)];
a[n_] := b[2*n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 18 2018, after Alois P. Heinz *)

Prog

(Python)
from sympy import divisors
from sympy.core.cache import cacheit
@cacheit
def b(n): return n if n<2 else sum([b(n-k)*sum([b(d)*d*(-1)**(k//d+1) for d in divisors(k)]) for k in range(1, n)])//(n-1)
def a(n): return b(2*n)
print([a(n) for n in range(31)]) # Indranil Ghosh, Mar 02 2018, after Maple program

Crossrefs

Bisection of A004111 (even part).

Cf. A100034, A299039, A299113.

Sequence in context: A366236 A276277 A355862 * A229042 A269484 A014277

Adjacent sequences: A299095 A299096 A299097 * A299099 A299100 A299101

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2018

Status

approved