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A299098 Number of rooted identity trees with 2n nodes. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A003454 A199241 A276277 * A229042 A269484 A014277

Adjacent sequences:  A299095 A299096 A299097 * A299099 A299100 A299101

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 02 2018

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)