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A053131
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Binomial coefficients C(2*n-8,9).
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6
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10, 220, 2002, 11440, 48620, 167960, 497420, 1307504, 3124550, 6906900, 14307150, 28048800, 52451256, 94143280, 163011640, 273438880, 445891810, 708930508, 1101716330, 1677106640, 2505433700, 3679075400, 5317936260
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OFFSET
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9,1
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COMMENTS
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a(n) = -A053123(n,9), n >= 9; a(n) := 0, n=0..8 (tenth column of shifted Chebyshev's S-triangle, decreasing order)
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 9..200
Milan Janjic, Two Enumerative Functions
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).
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FORMULA
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a(n) = binomial(2*n-8, 9) if n >= 9 else 0.
G.f.: (10+120*x+252*x^2+120*x^3+10*x^4)/(1-x)^10.
a(n) = 2*A053133(n).
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MATHEMATICA
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Binomial[2*Range[9, 40]-8, 9] (* Harvey P. Dale, Mar 19 2012 *)
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PROG
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(MAGMA)[Binomial(2*n-8, 9): n in [9..40]]; // Vincenzo Librandi, Oct 07 2011
(PARI) for(n=9, 50, print1(binomial(2*n-8, 9), ", ")) \\ G. C. Greubel, Aug 26 2018
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CROSSREFS
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Cf. A053123, A053130, A053133.
Sequence in context: A024291 A024292 A094420 * A334908 A166181 A199748
Adjacent sequences: A053128 A053129 A053130 * A053132 A053133 A053134
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang
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STATUS
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approved
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