cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A054327 Ninth column of Lanczos triangle A053125 (decreasing powers).

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%I A054327 #12 Sep 08 2022 08:45:00
%S A054327 9,660,20592,411840,6223360,77395968,833495040,8033304576,70882099200,
%T A054327 581979340800,4500640235520,33087710822400,232937484189696,
%U A054327 1579462143508480,10363761453957120,66060621396836352
%N A054327 Ninth column of Lanczos triangle A053125 (decreasing powers).
%D A054327 C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
%D A054327 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
%H A054327 G. C. Greubel, <a href="/A054327/b054327.txt">Table of n, a(n) for n = 0..1000</a>
%H A054327 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A054327 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (36, -576, 5376, -32256, 129024, -344064, 589824, -589824, 262144).
%F A054327 a(n) = 4^n*binomial(2*n+9, 8) = A053125(n+8, 8).
%F A054327 G.f.: (4*x+3)*(64*x^3+528*x^2+108*x+3)/(1-4*x)^9.
%t A054327 Table[4^n*Binomial[2*n+9, 8], {n,0,20}] (* _G. C. Greubel_, Jul 22 2019 *)
%o A054327 (PARI) vector(20, n, n--; 4^n*binomial(2*n+9,8)) \\ _G. C. Greubel_, Jul 22 2019
%o A054327 (Magma) [4^n*Binomial(2*n+9,8): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019
%o A054327 (Sage) [4^n*binomial(2*n+9,8) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019
%o A054327 (GAP) List([0..20], n-> 4^n*Binomial(2*n+9,8)); # _G. C. Greubel_, Jul 22 2019
%Y A054327 Cf. A053125, A054326.
%K A054327 nonn,easy
%O A054327 0,1
%A A054327 _Wolfdieter Lang_