A255523 Number of rooted identity trees with n n-colored non-root nodes.

1, 1, 5, 64, 1193, 30526, 991264, 39156244, 1824927697, 98125181461, 5983042467096, 408095177801851, 30797863537552547, 2548357838769171131, 229445851718471852031, 22334471403618839348901, 2337414940442888593612961, 261737726746663069945238177

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

Author

Alois P. Heinz, Feb 24 2015

Status

approved