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A054324 Sixth unsigned column of Lanczos triangle A053125 (decreasing powers).

%I A054324 #14 Sep 08 2022 08:45:00
%S A054324 6,224,4032,50688,512512,4472832,35094528,254017536,1725825024,
%T A054324 11142168576,68975329280,412216197120,2390853943296,13514114596864,
%U A054324 74693776244736,404792077713408,2155824474488832,11304491362025472
%N A054324 Sixth unsigned column of Lanczos triangle A053125 (decreasing powers).
%D A054324 C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
%D A054324 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
%H A054324 G. C. Greubel, <a href="/A054324/b054324.txt">Table of n, a(n) for n = 0..1000</a>
%H A054324 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A054324 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (24, -240, 1280, -3840, 6144, -4096).
%F A054324 a(n) = 4^n*binomial(2*n+6, 5) = -A053125(n+5, 5)= 2*A054330(n).
%F A054324 G.f.: 2*(3+4*x)*(1+12*x)/(1-4*x)^6.
%F A054324 E.g.f.: (2/15)*(45 +1500*x +8760*x^2 +15840*x^3 +10240*x^4 +2048*x^5) * exp(4*x). - _G. C. Greubel_, Jul 22 2019
%t A054324 Table[4^n Binomial[2n+6,5],{n,0,20}] (* or *) LinearRecurrence[{24,-240, 1280,-3840,6144,-4096},{6,224,4032,50688,512512,4472832},20] (* _Harvey P. Dale_, Jul 02 2017 *)
%o A054324 (PARI) vector(20, n, n--; 4^n*binomial(2*n+6, 5)) \\ _G. C. Greubel_, Jul 22 2019
%o A054324 (Magma) [4^n*Binomial(2*n+6, 5): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019
%o A054324 (Sage) [4^n*binomial(2*n+6, 5) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019
%o A054324 (GAP) List([0..20], n-> 4^n*Binomial(2*n+6, 5)); # _G. C. Greubel_, Jul 22 2019
%Y A054324 Cf. A053125, A054323, A054330.
%K A054324 nonn,easy
%O A054324 0,1
%A A054324 _Wolfdieter Lang_