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A337291
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a(n) = 3*binomial(4*n,n)/(4*n-1).
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4
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4, 12, 60, 364, 2448, 17556, 131560, 1017900, 8069424, 65204656, 535070172, 4446927732, 37353738800, 316621743480, 2704784196240, 23263187479980, 201275443944432, 1750651680235920, 15298438066553776, 134252511729576240, 1182622941581590080
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OFFSET
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1,1
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COMMENTS
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a(n) is the number of lattice paths from (0,0) to (3n,n) using only the steps (1,0) and (0,1) and whose only lattice points on the line y = x/3 are the path's endpoints. - Lucas A. Brown, Aug 21 2020
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LINKS
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FORMULA
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G.f.: 4*x*F(x)^3 where F(x) = 1 + x*F(x)^4 is the g.f. of A002293.
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MATHEMATICA
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PROG
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(PARI) a(n) = {3*binomial(4*n, n)/(4*n-1)} \\ Andrew Howroyd, Aug 21 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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