cp's OEIS Frontend

A054326 Eighth unsigned column of Lanczos triangle A053125 (decreasing powers).

%I A054326 #17 Sep 08 2022 08:45:00
%S A054326 8,480,12672,219648,2928640,32587776,317521920,2794192896,22682271744,
%T A054326 172438323200,1241555927040,8538764083200,56469693136896,
%U A054326 361019918516224,2240813287342080,13550896696786944,80073480481013760
%N A054326 Eighth unsigned column of Lanczos triangle A053125 (decreasing powers).
%D A054326 C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
%D A054326 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
%H A054326 Harvey P. Dale, <a href="/A054326/b054326.txt">Table of n, a(n) for n = 0..1000</a>
%H A054326 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A054326 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (32, -448, 3584, -17920, 57344, -114688, 131072, -65536).
%F A054326 a(n) = 4^n*binomial(2*n+8, 7) = -A053125(n+7, 7) = 8*A054331(n).
%F A054326 G.f.: 8*(4*x+1)*(16*x^2+24*x+1)/(1-4*x)^8.
%F A054326 a(0)=8, a(1)=480, a(2)=12672, a(3)=219648, a(4)=2928640, a(5)=32587776, a(6)=317521920, a(7)=2794192896, a(n) = 32*a(n-1) - 448*a(n-2) + 3584*a(n-3) - 17920*a(n-4) + 57344*a(n-5) - 114688*a(n-6) + 131072*a(n-7) - 65536*a(n-8). - _Harvey P. Dale_, Oct 23 2012
%t A054326 Table[4^n Binomial[2n+8,7],{n,0,20}] (* or *) LinearRecurrence[{32,-448, 3584,-17920,57344,-114688,131072,-65536},{8,480,12672,219648,2928640, 32587776,317521920,2794192896},20] (* _Harvey P. Dale_, Oct 23 2012 *)
%o A054326 (PARI) vector(20, n, n--; 4^n*binomial(2*n+8,7)) \\ _G. C. Greubel_, Jul 22 2019
%o A054326 (Magma) [4^n*Binomial(2*n+8,7): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019
%o A054326 (Sage) [4^n*binomial(2*n+8,7) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019
%o A054326 (GAP) List([0..20], n-> 4^n*Binomial(2*n+8,7)); # _G. C. Greubel_, Jul 22 2019
%Y A054326 Cf. A053125, A054325, A054331.
%K A054326 nonn,easy
%O A054326 0,1
%A A054326 _Wolfdieter Lang_