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

Author

Alois P. Heinz, Feb 24 2015

Keywords

• nonn

Examples

			a(2) = 5:
  o    o    o    o      o
  |    |    |    |     / \
  1    1    2    2    1   2
  |    |    |    |
  1    2    1    2
		

Links

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

Crossrefs

A diagonal of A255517.

Cf. A242375.

Programs

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 *)