A053129 Binomial coefficients C(2*n-6,7).

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, 491796152, 621216192

Offset

7,1

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).

Links

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 Janjić, Two Enumerative Functions, University of Banja Luka (Bosnia and Herzegovina, 2017).

Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Index entries for sequences related to Chebyshev polynomials.

Formula

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

From Amiram Eldar, Oct 21 2022: (Start)

Sum_{n>=7} 1/a(n) = 777/5 - 224*log(2).

Sum_{n>=7} (-1)^(n+1)/a(n) = 441/10 - 14*Pi. (End)

Maple

A053129:=n->binomial(2*n-6, 7); seq(A053129(n), n=7..50); # Wesley Ivan Hurt, Nov 14 2013

Mathematica

Table[Binomial[2 n - 6, 7], {n, 7, 50}] (* Wesley Ivan Hurt, Nov 14 2013 *)

Prog

(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

Crossrefs

Cf. A053123, A053128, A000973.

Sequence in context: A360978 A116008 A086302 * A249641 A045899 A165231

Adjacent sequences: A053126 A053127 A053128 * A053130 A053131 A053132

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved