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 A038055 Number of n-node rooted trees with nodes of 2 colors. 20
 2, 4, 14, 52, 214, 916, 4116, 18996, 89894, 433196, 2119904, 10503612, 52594476, 265713532, 1352796790, 6933598208, 35747017596, 185260197772, 964585369012, 5043220350012, 26467146038744, 139375369621960, 736229024863276, 3900074570513316, 20714056652990194 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 L. Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA] (2018). R. J. Mathar, Topologically distinct sets of non-intersecting circles in the plane, arXiv:1603.00077 [math.CO] (2016), Table 3. N. J. A. Sloane, Transforms Index entries for sequences related to rooted trees Index entries for sequences related to trees FORMULA Shifts left and halves under Euler transform. a(n) = 2*A000151(n). a(n) ~ c * d^n / n^(3/2), where d = A245870 = 5.646542616232949712892713516..., c = 0.41572319484583484264330698410170337587070758092051645875080558178621559423... . - Vaclav Kotesovec, Sep 11 2014, updated Dec 26 2020 MAPLE spec := [N, {N=Prod(bead, Set(N)), bead=Union(R, B), R=Atom, B=Atom}]; [seq(combstruct[count](spec, size=n), n=1..40)]; # second Maple program: with(numtheory): a:= proc(n) option remember; `if`(n<2, 2*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, May 11 2014 MATHEMATICA a[n_] := a[n] = If[n<2, 2*n, (Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j], {j, 1, n-1}])/(n-1)]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 25 2015, after Alois P. Heinz *) a[1] = 2; a[n_] := a[n] = Sum[k a[k] a[n - m k]/(n-1), {k, n}, {m, (n-1)/k}]; Table[a[n], {n, 30}] (* Vladimir Reshetnikov, Aug 12 2016 *) PROG (PARI) seq(N) = {my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 2/n * sum(i=1, n, sumdiv(i, d, d*A[d]) * A[n-i+1] ) ); 2*A} \\ Andrew Howroyd, May 12 2018 CROSSREFS Cf. A000081, A038056-A038062, A271878 (multisets). Cf. A245870. Sequence in context: A316363 A295760 A129876 * A006385 A322859 A183949 Adjacent sequences: A038052 A038053 A038054 * A038056 A038057 A038058 KEYWORD nonn,eigen,nice,easy AUTHOR Christian G. Bower, Jan 04 1999 STATUS approved

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Last modified September 8 16:32 EDT 2024. Contains 375753 sequences. (Running on oeis4.)