A299113 -id:A299113 - cp's OEIS frontend

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

Alois P. Heinz, Feb 02 2018

nonn

			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

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

Bisection of A004111 (even part).

Cf. A100034, A299039, A299113.

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);

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 *)

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

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

A100427 Bisection of A000081 (odd part).

Original entry on oeis.org

1, 2, 9, 48, 286, 1842, 12486, 87811, 634847, 4688676, 35221832, 268282855, 2067174645, 16083734329, 126186554308, 997171512998, 7929819784355, 63411730258053, 509588049810620, 4113254119923150, 33333125878283632, 271097737169671824, 2212039245722726118

Offset: 0

N. J. A. Sloane, Nov 20 2004

Alois P. Heinz, Table of n, a(n) for n = 0..400

Cf. A000081, A100034, A299113.

with(numtheory):
b:= proc(n) option remember; local d, j; `if`(n<2, n,
      (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
    end:
a:= n-> b(2*n+1):
seq(a(n), n=0..50);  # Alois P. Heinz, May 16 2013

b[n_] := b[n] = If[n <= 1, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]; a[n_] := b[2*n+1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)

More terms from Joshua Zucker, May 12 2006

cp's OEIS Frontend

A299098 Number of rooted identity trees with 2n nodes.

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