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A242375 Number of rooted trees with n n-colored non-root nodes. 3
1, 1, 7, 82, 1499, 37476, 1200705, 46990952, 2175619923, 116400215521, 7069820334023, 480722969498938, 36186340018129392, 2987845924408179654, 268530017303221572650, 26098422892000807053155, 2727654868575748827350403, 305075571192329680642519141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) ~ c * exp(n) * n^(n-3/2), where c = 1.160358615244339554387715747... . - Vaclav Kotesovec, Aug 28 2014

EXAMPLE

a(2) = 7:

o    o    o    o      o        o        o

|    |    |    |     / \      / \      / \

1    1    2    2    1   1    1   2    2   2

|    |    |    |

1    2    1    2

MAPLE

with(numtheory):

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

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

    end:

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

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

MATHEMATICA

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)];

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

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Mar 21 2017, translated from Maple *)

CROSSREFS

A diagonal of A242249.

Cf. A255523.

Sequence in context: A191804 A243672 A268653 * A333984 A244821 A304591

Adjacent sequences:  A242372 A242373 A242374 * A242376 A242377 A242378

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 12 2014

STATUS

approved

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Last modified September 28 21:56 EDT 2020. Contains 337415 sequences. (Running on oeis4.)