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A242375 Number of rooted trees with n n-colored non-root nodes. 3

%I

%S 1,1,7,82,1499,37476,1200705,46990952,2175619923,116400215521,

%T 7069820334023,480722969498938,36186340018129392,2987845924408179654,

%U 268530017303221572650,26098422892000807053155,2727654868575748827350403,305075571192329680642519141

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

%H Alois P. Heinz, <a href="/A242375/b242375.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ c * exp(n) * n^(n-3/2), where c = 1.160358615244339554387715747... . - _Vaclav Kotesovec_, Aug 28 2014

%e a(2) = 7:

%e o o o o o o o

%e | | | | / \ / \ / \

%e 1 1 2 2 1 1 1 2 2 2

%e | | | |

%e 1 2 1 2

%p with(numtheory):

%p b:= proc(n, k) option remember; `if`(n<2, n, (add(add(d*

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

%p end:

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

%p seq(a(n), n=0..20);

%t b[n_, k_] := b[n, k] = If[n < 2, n, (Sum[Sum[d*b[d, k], {d, Divisors[j]}] * b[n - j, k]*k, {j, 1, n - 1}])/(n - 1)];

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

%t Table[a[n], {n, 0, 20}] (* _Jean-Fran├žois Alcover_, Mar 21 2017, translated from Maple *)

%Y A diagonal of A242249.

%Y Cf. A255523.

%K nonn,changed

%O 0,3

%A _Alois P. Heinz_, May 12 2014

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Last modified February 5 08:15 EST 2023. Contains 360082 sequences. (Running on oeis4.)