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A036652
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Number of bicentered 6-valent trees with n nodes.
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2
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0, 0, 1, 0, 1, 1, 3, 4, 11, 19, 49, 103, 254, 583, 1445, 3506, 8815, 22082, 56286, 143822, 371354, 963250, 2516822, 6607348, 17440933, 46233833, 123090070, 328923702, 882114742, 2373351473, 6405275496, 17336081498, 47047112028
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OFFSET
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0,7
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LINKS
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FORMULA
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MATHEMATICA
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n = 20; (* algorithm from Rains and Sloane *)
S5[f_, h_, x_] := f[h, x]^5/120 + f[h, x]^3 f[h, x^2]/12 + f[h, x]^2 f[h, x^3]/6 + f[h, x] f[h, x^2]^2/8 + f[h, x] f[h, x^4]/4 + f[h, x^2] f[h, x^3]/6 + f[h, x^5]/5;
T[-1, z_] := 1; T[h_, z_] := T[h, z] = Table[z^k, {k, 0, n}].Take[CoefficientList[z^(n+1) + 1 + S5[T, h-1, z]z, z], n+1];
Sum[Take[CoefficientList[z^(n+1) + (T[h, z] - T[h-1, z])^2/2 + (T[h, z^2] - T[h-1, z^2])/2, z], n+1], {h, 0, n/2}] (* Robert A. Russell, Sep 15 2018 *)
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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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