%I #13 Feb 02 2023 17:27:44

%S 1,1,5,64,1193,30526,991264,39156244,1824927697,98125181461,

%T 5983042467096,408095177801851,30797863537552547,2548357838769171131,

%U 229445851718471852031,22334471403618839348901,2337414940442888593612961,261737726746663069945238177

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

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

%e a(2) = 5:

%e o o o o o

%e | | | | / \

%e 1 1 2 2 1 2

%e | | | |

%e 1 2 1 2

%p with(numtheory):

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

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

%p end:

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

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

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

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

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

%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 29 2022, after _Alois P. Heinz_ *)

%Y A diagonal of A255517.

%Y Cf. A242375.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 24 2015