The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A255523

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A255523

Number of rooted identity trees with n n-colored non-root nodes.
(history; published version)

#13 by Alois P. Heinz at Thu Feb 02 17:27:44 EST 2023

STATUS

editing

approved

#12 by Alois P. Heinz at Thu Feb 02 17:27:41 EST 2023

EXAMPLE

o o o o o

| | | | / \

1 1 2 2 1 2

| | | |

1 2 1 2

STATUS

approved

editing

#11 by Peter Luschny at Fri Apr 29 05:50:49 EDT 2022

STATUS

reviewed

approved

#10 by Michel Marcus at Fri Apr 29 05:26:25 EDT 2022

STATUS

proposed

reviewed

#9 by Jean-François Alcover at Fri Apr 29 04:38:12 EDT 2022

STATUS

editing

proposed

#8 by Jean-François Alcover at Fri Apr 29 04:38:06 EDT 2022

MATHEMATICA

A[n_, k_] := A[n, k] = If[n < 2, n, Sum[A[n-j, k]*Sum[

k*A[d, k]*d*(-1)^(j/d+1), {d, Divisors[j]}], {j, 1, n-1}]/(n-1)];

a[n_] := A[n+1, n];

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 29 2022, after Alois P. Heinz *)

STATUS

approved

editing

#7 by Alois P. Heinz at Tue Feb 24 14:52:08 EST 2015

STATUS

editing

approved

#6 by Alois P. Heinz at Tue Feb 24 14:52:05 EST 2015

EXAMPLE

a(2) = 5:

o o o o o

| | | | / \

1 1 2 2 1 2

| | | |

1 2 1 2

STATUS

approved

editing

#5 by Alois P. Heinz at Tue Feb 24 10:49:26 EST 2015

STATUS

editing

approved

#4 by Alois P. Heinz at Tue Feb 24 10:39:29 EST 2015

LINKS

Alois P. Heinz, <a href="/A255523/b255523.txt">Table of n, a(n) for n = 0..300</a>

MAPLE

with(numtheory):

A:= proc(n, k) option remember; `if`(n<2, n, add(A(n-j, k)*add(

k*A(d, k)*d*(-1)^(j/d+1), d=divisors(j)), j=1..n-1)/(n-1))

end:

a:= n-> A(n+1, n):

seq(a(n), n=0..25);