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A214203
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Number of rooted planar binary unlabeled trees with n leaves and caterpillar index <= 5.
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8
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0, 1, 1, 2, 5, 14, 26, 100, 333, 1110, 3742, 12764, 44258, 154636, 544660, 1932360, 6900029, 24780390, 89445174, 324326060, 1180834390, 4315287140, 15823305516, 58200045432, 214672363410, 793883691004, 2942917457772, 10933569255832, 40704185771812, 151826357818840, 567322837830824, 2123429246035600, 7960199797453213, 29884582184913542
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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)*(1 - Sqrt[1 - 4*x + 64*x^6]) + O[x]^34 // 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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