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%I #46 Oct 21 2022 09:45:16
%S 8,120,792,3432,11440,31824,77520,170544,346104,657800,1184040,
%T 2035800,3365856,5379616,8347680,12620256,18643560,26978328,38320568,
%U 53524680,73629072,99884400,133784560,177100560,231917400,300674088,386206920,491796152,621216192
%N Binomial coefficients C(2*n-6,7).
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).
%H Vincenzo Librandi, <a href="/A053129/b053129.txt">Table of n, a(n) for n = 7..200</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H Milan Janjić, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>, University of Banja Luka (Bosnia and Herzegovina, 2017).
%H Ângela Mestre and José Agapito, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Mestre/mestre2.html">Square Matrices Generated by Sequences of Riordan Arrays</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.
%F a(n) = binomial(2*n-6, 7) if n >= 7 else 0.
%F a(n) = -A053123(n,7), n >= 7; a(n) := 0, n=0..6, (eighth column of shifted Chebyshev's S-triangle, decreasing order).
%F a(n) = 8*A000973(n).
%F G.f.: (8+56*x+56*x^2+8*x^3)/(1-x)^8.
%F 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
%F From _Amiram Eldar_, Oct 21 2022: (Start)
%F Sum_{n>=7} 1/a(n) = 777/5 - 224*log(2).
%F Sum_{n>=7} (-1)^(n+1)/a(n) = 441/10 - 14*Pi. (End)
%p A053129:=n->binomial(2*n-6,7); seq(A053129(n), n=7..50); # _Wesley Ivan Hurt_, Nov 14 2013
%t Table[Binomial[2 n - 6, 7], {n, 7, 50}] (* _Wesley Ivan Hurt_, Nov 14 2013 *)
%o (Magma) [Binomial(2*n-6,7): n in [7..40]]; // _Vincenzo Librandi_, Oct 07 2011
%o (PARI) for(n=7, 50, print1(binomial(2*n-6,7), ", ")) \\ _G. C. Greubel_, Aug 26 2018
%Y Cf. A053123, A053128, A000973.
%K nonn,easy
%O 7,1
%A _Wolfdieter Lang_
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