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%I #29 Aug 03 2020 05:52:00
%S 3,9,45,246,1485,9432,62625,428319,3000393,21410436,155106693,
%T 1137703869,8432624850,63060142671,475196487363,3604851603690,
%U 27507181503069,210988219961637,1625848092941463,12580709718788622,97714211996345868,761528782558088202
%N Number of rooted trees with 3-colored nodes.
%C Shifts left and divides by 3 under Euler transform.
%H L. Foissy, <a href="https://arxiv.org/abs/1811.07572">Algebraic structures on typed decorated rooted trees</a>, arXiv:1811.07572 [math.RA] (2018).
%H R. J. Mathar, <a href="http://arxiv.org/abs/1603.00077">Topologically distinct sets of non-intersecting circles in the plane</a>, arXiv:1603.00077 [math.CO] (2016), Table 4.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) = 3 * A006964(n).
%p with(numtheory): a:= proc(n) option remember; `if`(n<2, 3*n, (add(add(d*a(d), d=divisors(j)) *a(n-j), j=1..n-1))/ (n-1)) end: seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 06 2008
%t a[n_] := a[n] = If[n<2, 3*n, Sum[Sum[d*a[d], {d, Divisors[j]}] *a[n-j], {j, 1, n-1}]/(n-1)]; Array[a, 30] (* _Jean-François Alcover_, Feb 24 2016, after _Alois P. Heinz_ *)
%Y Cf. A000081, A038055-A038062, A271879 (multisets).
%K nonn,eigen
%O 1,1
%A _Christian G. Bower_, Jan 04 1999
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