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A214199
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Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 3.
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8
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0, 0, 0, 2, 0, 4, 12, 36, 120, 392, 1288, 4284, 14304, 48024, 162024, 548872, 1866416, 6368464, 21797776, 74822636, 257513344, 888439192, 3072153864, 10645835384, 36964041872, 128584760560, 448087042160, 1564065659608, 5467992829120, 19144550862960, 67123334707984, 235658063191312, 828405764175712, 2915610778184352, 10273466501139232, 36239527330228044
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OFFSET
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0,4
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LINKS
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MAPLE
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C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
Sm:=k->seriestolist(series(Fm(k), x, 50));
Fp:=k->C-Fm(k-1);
Sp:=k->seriestolist(series(Fp(k), x, 50));
F:=k->Fm(k)-Fm(k-1);
S:=k->seriestolist(series(F(k), x, 50));
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MATHEMATICA
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(1/2)*(Sqrt[1-4*x+8*x^3]-Sqrt[1-4*x+16*x^4])+O[x]^36 // CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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