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 A126218 Triangle read by rows: T(n,k) is the number of 0-1-2 trees (i.e., ordered trees with all vertices of outdegree at most two) with n edges and k pairs of adjacent vertices of outdegree 2. 0
 1, 1, 2, 4, 7, 2, 13, 8, 26, 20, 5, 52, 50, 25, 104, 130, 75, 14, 212, 322, 217, 84, 438, 770, 644, 294, 42, 910, 1836, 1806, 952, 294, 1903, 4362, 4830, 3108, 1176, 132, 4009, 10268, 12738, 9576, 4188, 1056, 8494, 24032, 33219, 27948, 14760, 4752, 429, 18080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row n has floor(n/2) terms (n >= 2). Row sums are the Motzkin numbers (A001006). T(n,1) = A023431(n+1). Sum_{k=0..floor(n/2)-1} k*T(n,k) = 2*A014532(n-3) (n >= 4). LINKS Table of n, a(n) for n=0..51. FORMULA G.f.: G = G(t,z) satisfies G = 1 + zG + z^2*(1 + zG + t(G-1-zG))^2 (see the Maple program for the explicit expression). EXAMPLE Triangle starts: 1; 1; 2; 4; 7, 2; 13, 8; 26, 20, 5; 52, 50, 25; MAPLE G:=1/2*(2*z^2*t^2-z+4*z^3*t-2*z^3*t^2-2*z^2*t-2*z^3+1-sqrt(1+4*z^3*t-4*z^2*t+z^2-2*z-4*z^3))/z^2/(z*t-t-z)^2: Gser:=simplify(series(G, z=0, 18)): for n from 0 to 15 do P[n]:=sort(coeff(Gser, z, n)) od: 1; 1; for n from 2 to 15 do seq(coeff(P[n], t, j), j=0..floor(n/2)-1) od; # yields sequence in triangular form CROSSREFS Cf. A001006, A014532, A023431. Sequence in context: A244262 A166531 A133292 * A086330 A098283 A373786 Adjacent sequences: A126215 A126216 A126217 * A126219 A126220 A126221 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Dec 24 2006 STATUS approved

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Last modified September 12 11:46 EDT 2024. Contains 375851 sequences. (Running on oeis4.)