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%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
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