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 A038059 Number of rooted trees with 3-colored nodes. 3
 3, 9, 45, 246, 1485, 9432, 62625, 428319, 3000393, 21410436, 155106693, 1137703869, 8432624850, 63060142671, 475196487363, 3604851603690, 27507181503069, 210988219961637, 1625848092941463, 12580709718788622, 97714211996345868, 761528782558088202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Shifts left and divides by 3 under Euler transform. LINKS L. Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 (2018) R. J. Mathar, Topologically distinct sets of non-intersecting circles in the plane, arXiv:1603.00077 (2016), Table 4. N. J. A. Sloane, Transforms FORMULA a(n) = 3 * A006964(n). MAPLE 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 MATHEMATICA 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 *) CROSSREFS Cf. A000081, A038055-A038062. Sequence in context: A247006 A103620 A138315 * A174318 A004990 A027616 Adjacent sequences:  A038056 A038057 A038058 * A038060 A038061 A038062 KEYWORD nonn,eigen AUTHOR Christian G. Bower, Jan 04 1999 STATUS approved

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Last modified January 22 16:45 EST 2019. Contains 319364 sequences. (Running on oeis4.)