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A053129
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Binomial coefficients C(2*n-6,7).
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6
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8, 120, 792, 3432, 11440, 31824, 77520, 170544, 346104, 657800, 1184040, 2035800, 3365856, 5379616, 8347680, 12620256, 18643560, 26978328, 38320568, 53524680, 73629072, 99884400, 133784560, 177100560, 231917400, 300674088, 386206920
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OFFSET
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7,1
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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 = 7..200
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].
Milan Janjic, Two Enumerative Functions, University of Banja Luka (Bosnia and Herzegovina, 2017).
Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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a(n) = binomial(2*n-6, 7) if n >= 7 else 0.
a(n) = -A053123(n,7), n >= 7; a(n) := 0, n=0..6, (eighth column of shifted Chebyshev's S-triangle, decreasing order).
a(n) = 8*A000973(n).
G.f.: (8+56*x+56*x^2+8*x^3)/(1-x)^8.
a(n) = (n-6)*(n-5)*(n-4)*(n-3)*(2*n-11)*(2*n-9)*(2*n-7)/315. - Wesley Ivan Hurt, Mar 25 2020
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MAPLE
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A053129:=n->binomial(2*n-6, 7); seq(A053129(n), n=7..50); # Wesley Ivan Hurt, Nov 14 2013
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MATHEMATICA
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Table[Binomial[2 n - 6, 7], {n, 7, 50}] (* Wesley Ivan Hurt, Nov 14 2013 *)
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PROG
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(MAGMA) [Binomial(2*n-6, 7): n in [7..40]]; // Vincenzo Librandi, Oct 07 2011
(PARI) for(n=7, 50, print1(binomial(2*n-6, 7), ", ")) \\ G. C. Greubel, Aug 26 2018
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CROSSREFS
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Cf. A053123, A053128, A000973.
Sequence in context: A228752 A116008 A086302 * A249641 A045899 A165231
Adjacent sequences: A053126 A053127 A053128 * A053130 A053131 A053132
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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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