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%I #12 Sep 08 2022 08:45:00
%S 7,336,7392,109824,1281280,12673024,111132672,889061376,6615662592,
%T 46425702400,310388981760,1992378286080,12352745373696,74327630282752,
%U 435713694760960,2496217812566016,14012859084177408,77247357640507392
%N Seventh column of Lanczos triangle A053125 (decreasing powers).
%D C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
%D Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
%H G. C. Greubel, <a href="/A054325/b054325.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28, -336, 2240, -8960, 21504, -28672, 16384).
%F a(n) = 4^n*binomial(2*n+7, 6) = A053125(n+6, 6).
%F G.f.: (7 +140*x +336*x^2 +64*x^3)/(1-4*x)^7.
%t Table[4^n*Binomial[2*n+7, 6], {n,0,20}] (* _G. C. Greubel_, Jul 22 2019 *)
%o (PARI) vector(20, n, n--; 4^n*binomial(2*n+7, 6)) \\ _G. C. Greubel_, Jul 22 2019
%o (Magma) [4^n*Binomial(2*n+7, 6): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019
%o (Sage) [4^n*binomial(2*n+7, 6) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019
%o (GAP) List([0..20], n-> 4^n*Binomial(2*n+7, 6)); # _G. C. Greubel_, Jul 22 2019
%Y Cf. A053125, A054324.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_
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