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

%I A255523 #13 Feb 02 2023 17:27:44
%S A255523 1,1,5,64,1193,30526,991264,39156244,1824927697,98125181461,
%T A255523 5983042467096,408095177801851,30797863537552547,2548357838769171131,
%U A255523 229445851718471852031,22334471403618839348901,2337414940442888593612961,261737726746663069945238177
%N A255523 Number of rooted identity trees with n n-colored non-root nodes.
%H A255523 Alois P. Heinz, <a href="/A255523/b255523.txt">Table of n, a(n) for n = 0..300</a>
%e A255523 a(2) = 5:
%e A255523   o    o    o    o      o
%e A255523   |    |    |    |     / \
%e A255523   1    1    2    2    1   2
%e A255523   |    |    |    |
%e A255523   1    2    1    2
%p A255523 with(numtheory):
%p A255523 A:= proc(n, k) option remember; `if`(n<2, n, add(A(n-j, k)*add(
%p A255523       k*A(d, k)*d*(-1)^(j/d+1), d=divisors(j)), j=1..n-1)/(n-1))
%p A255523     end:
%p A255523 a:= n-> A(n+1, n):
%p A255523 seq(a(n), n=0..25);
%t A255523 A[n_, k_] := A[n, k] = If[n < 2, n, Sum[A[n-j, k]*Sum[
%t A255523      k*A[d, k]*d*(-1)^(j/d+1), {d, Divisors[j]}], {j, 1, n-1}]/(n-1)];
%t A255523 a[n_] := A[n+1, n];
%t A255523 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 29 2022, after _Alois P. Heinz_ *)
%Y A255523 A diagonal of A255517.
%Y A255523 Cf. A242375.
%K A255523 nonn
%O A255523 0,3
%A A255523 _Alois P. Heinz_, Feb 24 2015