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A054328 Tenth unsigned column of Lanczos triangle A053125 (decreasing powers). 2

%I

%S 10,880,32032,732160,12446720,171991040,2037432320,21422145536,

%T 204770508800,1810602393600,15002134118400,117645194035200,

%U 879986051383296,6317848574033920,43758103916707840,293602761763717120

%N Tenth unsigned 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="/A054328/b054328.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_10">Index entries for linear recurrences with constant coefficients</a>, signature (40, -720, 7680, -53760, 258048, -860160, 1966080, -2949120, 2621440, -1048576).

%F a(n) = 4^n*binomial(2*n+10, 9)= -A053125(n+9, 9) = 2* A054332(n).

%F G.f. 2*(1+40*x+80*x^2)*(5+40*x+16*x^2)/(1-4*x)^10.

%t CoefficientList[Series[2(1+40x+80x^2)(5+40x+16x^2)/(1-4x)^10,{x,0,20}],x] (* _Harvey P. Dale_, Feb 28 2011 *)

%t Table[4^n*Binomial[2*n+10, 9], {n,0,20}] (* _G. C. Greubel_, Jul 22 2019 *)

%o (PARI) vector(20, n, n--; 4^n*binomial(2*n+10,9)) \\ _G. C. Greubel_, Jul 22 2019

%o (MAGMA) [4^n*Binomial(2*n+10,9): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019

%o (Sage) [4^n*binomial(2*n+10,9) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019

%o (GAP) List([0..20], n-> 4^n*Binomial(2*n+10,9)); # _G. C. Greubel_, Jul 22 2019

%Y Cf. A053125, A054327, A054332.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_

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Last modified December 14 01:41 EST 2019. Contains 329978 sequences. (Running on oeis4.)