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Search: id:A127158
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| A127158 |
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Triangle read by rows: T(n,k) is the number of ordered trees with n edges and having k branches of length 1 starting from the root (0<=k<=n). |
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+0
3
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| 1, 0, 1, 1, 0, 1, 1, 3, 0, 1, 3, 5, 5, 0, 1, 7, 18, 9, 7, 0, 1, 20, 52, 37, 13, 9, 0, 1, 59, 168, 113, 60, 17, 11, 0, 1, 184, 546, 388, 190, 87, 21, 13, 0, 1, 593, 1826, 1313, 688, 283, 118, 25, 15, 0, 1, 1964, 6211, 4545, 2408, 1076, 392, 153, 29, 17, 0, 1, 6642, 21459
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OFFSET
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0,8
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COMMENT
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Row sums are the Catalan numbers (A000108). T(n,0)=A030238(n-2) for n>=2. Sum(k*T(n,k),k=0..n)=A026012(n-1) for n>=1.
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FORMULA
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G.f.= 1/(1-tzC+tz^2*C-z^2*C), where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
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Triangle starts:
1;
0,1;
1,0,1;
1,3,0,1;
3,5,5,0,1;
7,18,9,7,0,1;
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MAPLE
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C:=(1-sqrt(1-4*z))/2/z: G:=1/(1-t*z*C+t*z^2*C-z^2*C): Gser:=simplify(series(G, z=0, 15)): for n from 0 to 12 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 12 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000108, A030238, A026012.
Sequence in context: A121481 A121469 A091867 this_sequence A112367 A035623 A083857
Adjacent sequences: A127155 A127156 A127157 this_sequence A127159 A127160 A127161
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007
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