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A255523 Number of rooted identity trees with n n-colored non-root nodes. 3
1, 1, 5, 64, 1193, 30526, 991264, 39156244, 1824927697, 98125181461, 5983042467096, 408095177801851, 30797863537552547, 2548357838769171131, 229445851718471852031, 22334471403618839348901, 2337414940442888593612961, 261737726746663069945238177 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

EXAMPLE

a(2) = 5:

o o o o o

| | | | / \

1 1 2 2 1 2

| | | |

1 2 1 2

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);

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 *)

CROSSREFS

A diagonal of A255517.

Cf. A242375.

Sequence in context: A054937 A302993 A266095 * A193222 A274265 A073179

Adjacent sequences: A255520 A255521 A255522 * A255524 A255525 A255526

KEYWORD

nonn,changed

AUTHOR

Alois P. Heinz, Feb 24 2015

STATUS

approved

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Last modified February 8 03:07 EST 2023. Contains 360134 sequences. (Running on oeis4.)