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Search: id:A126191
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| A126191 |
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Triangle read by rows: number of 0-1-2 trees (i.e. ordered trees with vertices of outdegrees 0, 1, or 2) with n edges and exactly k vertices that have 2 children, both being leaves (n>=0, 0<=k<=floor((n+2)/4)). |
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1
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| 1, 1, 1, 1, 3, 1, 6, 3, 14, 7, 33, 17, 1, 79, 45, 3, 194, 117, 12, 482, 313, 40, 1214, 843, 129, 2, 3090, 2287, 411, 10, 7936, 6247, 1278, 50, 20544, 17139, 3942, 210, 53545, 47219, 12045, 820, 5, 140399, 130527, 36559, 3052, 35, 370098, 361851, 110388
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OFFSET
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0,5
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COMMENT
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Row n has 1+floor((n+2)/4) terms. Row sums yield the Motzkin numbers (A001006). T(n,0)=A025243(n+2) (n>=1). Sum(k*T(n,k),k=0..floor((n+2)/4))=A002426(n-2) (the central trinomial coefficients).
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FORMULA
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G.f.=G=G(t,z) satisfies G=1+zG+z^2*(G^2-1+t).
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MAPLE
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G:=(1-z-sqrt(1-2*z-3*z^2+4*z^4-4*z^4*t))/2/z^2: Gser:=simplify(series(G, z=0, 21)): for n from 0 to 17 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 17 do seq(coeff(P[n], t, j), j=0..floor((n+2)/4)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001006, A025243, A002426.
Sequence in context: A008795 A165188 A132180 this_sequence A070883 A120029 A133110
Adjacent sequences: A126188 A126189 A126190 this_sequence A126192 A126193 A126194
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 27 2006
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