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%I #11 Sep 08 2022 08:45:00
%S 3,112,2016,25344,256256,2236416,17547264,127008768,862912512,
%T 5571084288,34487664640,206108098560,1195426971648,6757057298432,
%U 37346888122368,202396038856704,1077912237244416,5652245681012736
%N One half of sixth unsigned column of Lanczos' triangle A053125.
%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="/A054330/b054330.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (24, -240, 1280, -3840, 6144, -4096).
%F a(n)= 2^(2*n-1)*binomial(2*n+6, 5) = -A053125(n+5, 5)/2 = A054324(n)/2.
%F G.f.: (4*x+3)*(12*x+1)/(1-4*x)^6.
%F E.g.f.: (90 + 3000*x + 17520*x^2 + 31680*x^3 + 20480*x^4 + 4096*x^5)* exp(4*x)/30. - _G. C. Greubel_, Jul 22 2019
%t Table[2^(2*n-1)*Binomial[2*n+6, 5], {n,0,20}] (* _G. C. Greubel_, Jul 22 2019 *)
%o (PARI) vector(20, n, n--; 2^(2*n-1)*binomial(2*n+6,5)) \\ _G. C. Greubel_, Jul 22 2019
%o (Magma) [2^(2*n-1)*Binomial(2*n+6,5): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019
%o (Sage) [2^(2*n-1)*binomial(2*n+6,5) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019
%o (GAP) List([0..20], n-> 2^(2*n-1)*Binomial(2*n+6,5)); # _G. C. Greubel_, Jul 22 2019
%Y Cf. A054324, A053125.
%K easy,nonn
%O 0,1
%A _Wolfdieter Lang_
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