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A214201
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Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 4.
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8
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0, 0, 0, 0, 4, 8, 24, 80, 264, 912, 3216, 11488, 41528, 151408, 555792, 2051808, 7610384, 28341536, 105914784, 397028544, 1492351576, 5623204528, 21235347856, 80355038176, 304630332528, 1156851587552, 4400205758176, 16761475403328, 63937267846704, 244209062245984, 933904716768672, 3575584117620416, 13704666128328736, 52582688861676096
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OFFSET
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0,5
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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+16*x^4]-Sqrt[1-4*x]) + 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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