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A036649
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Number of bicentered 5-valent trees with n nodes.
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2
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0, 0, 1, 0, 1, 1, 3, 4, 10, 18, 46, 95, 231, 524, 1287, 3095, 7713, 19125, 48258, 122026, 311935, 801061, 2072629, 5387753, 14081981, 36959506, 97419796, 257724555, 684254908, 1822560590, 4869517848, 13047469920, 35053803135
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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 = 30; (* algorithm from Rains and Sloane *)
S4[f_, h_, x_] := f[h, x]^4/24 + f[h, x]^2 f[h, x^2]/4 + f[h, x] f[h, x^3]/3 + f[h, x^2]^2/8 + f[h, x^4]/4;
T[-1, z_] := 1; T[h_, z_] := T[h, z] = Table[z^k, {k, 0, n}].Take[CoefficientList[z^(n+1) + 1 + S4[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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