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%I #15 Dec 13 2018 11:33:33
%S 4,16,104,752,5996,50512,444256,4027360,37383044,353486320,3393093696,
%T 32976302800,323839605124,3208549483216,32033691247528,
%U 321955764477936,3254812520854980,33075467402453872,337670437247448728,3461635652745799136,35620112071990294784
%N Number of unlabeled rooted trees with n 4-colored nodes.
%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).
%H L. Foissy, <a href="https://arxiv.org/abs/1811.07572">Algebraic structures on typed decorated rooted trees</a>, arXiv:1811.07572 (2018)
%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>
%F Shifts left and divides by 4 under EULER transform. a(n) = A136794(n)*2 = A052763(n)*4.
%p with(numtheory):
%p a:= proc(n) option remember; `if`(n<2, n*4, (add(add(d*
%p a(d), d=divisors(j))*a(n-j), j=1..n-1))/(n-1))
%p end:
%p seq(a(n), n=1..25); # _Alois P. Heinz_, May 16 2014
%t a[1] = 4; a[n_] := a[n] = Sum[ Sum[ d*a[d], {d, Divisors[j]}]*a[n-j], {j, 1, n-1}]/(n-1); Table[a[n], {n, 1, 25}] (* _Jean-François Alcover_, Feb 24 2015, after _Alois P. Heinz_ *)
%K nonn
%O 1,1
%A _Christian G. Bower_, Jan 21 2008
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