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 A005754 Number of planted identity matched trees with n nodes. (Formerly M1765) 11
 1, 1, 2, 7, 24, 95, 388, 1650, 7183, 31965, 144502, 662241, 3068942, 14358678, 67729973, 321759461, 1538076291, 7392775328, 35707198905, 173221206284, 843634142771, 4123376617009, 20218897206392, 99436453714990, 490355165178472, 2424146632435852 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Number of rooted identity trees with n nodes and edges not attached to root are 2-colored or oriented. - Christian G. Bower, Dec 15 1999 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..400 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 430 R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1991), 93-104. R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1981), 97. (Annotated scanned copy) N. J. A. Sloane, Transforms Index entries for sequences related to rooted trees FORMULA a(n+1) is Weigh transform of A005753. - Christian G. Bower, Dec 15 1999 a(n) ~ c * d^n / n^(3/2), where d = A246312 = 5.2490324912281705791649522..., c = 0.05927840588836202377824646... . - Vaclav Kotesovec, Aug 25 2014 G.f. A(x) satisfies: A(x) = x * exp( A(x)^2/x - A(x^2)^2/(2*x^2) + A(x^3)^2/(3*x^3) - A(x^4)^2/(4*x^4) + ... ). - Ilya Gutkovskiy, May 26 2023 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(binomial(2*b((i-1)\$2), j)*b(n-i*j, i-1), j=0..n/i))) end: g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(binomial(b((i-1)\$2), j)*g(n-i*j, i-1), j=0..n/i))) end: a:= n-> g((n-1)\$2): seq(a(n), n=1..30); # Alois P. Heinz, Aug 01 2013 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[2*b[i-1, i-1], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; g[n_, i_] := g[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i-1, i-1], j]*g[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := g[n-1, n-1]; Table[a[n], {n, 1, 30}] // FullSimplify (* Jean-François Alcover, Dec 02 2013, translated from Alois P. Heinz's Maple program *) CROSSREFS Cf. A005753, A102755, A246312. Sequence in context: A150421 A150422 A137952 * A007162 A150423 A150424 Adjacent sequences: A005751 A005752 A005753 * A005755 A005756 A005757 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Christian G. Bower, Dec 15 1999 STATUS approved

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Last modified February 26 19:43 EST 2024. Contains 370352 sequences. (Running on oeis4.)