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A214205
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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, 0, 0, 0, 0, 8, 0, 16, 64, 240, 832, 2976, 11008, 40624, 150400, 559584, 2090112, 7832928, 29432704, 110863680, 418479104, 1582628656, 5995379456, 22746329952, 86417102720, 328720669216, 1251831214976, 4772155518656, 18209463672320, 69544295350240, 265814912973056, 1016776398337728, 3892040452165888, 14907843267549376
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OFFSET
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0,6
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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 + 32*x^5] - 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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