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A054331 One eighth of eighth unsigned column of Lanczos' triangle A053125.

%I A054331 #21 Feb 02 2023 18:28:56
%S A054331 1,60,1584,27456,366080,4073472,39690240,349274112,2835283968,
%T A054331 21554790400,155194490880,1067345510400,7058711642112,45127489814528,
%U A054331 280101660917760,1693862087098368,10009185060126720,57935518230380544
%N A054331 One eighth of eighth unsigned column of Lanczos' triangle A053125.
%D A054331 C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
%D A054331 Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
%H A054331 G. C. Greubel, <a href="/A054331/b054331.txt">Table of n, a(n) for n = 0..1000</a>
%H A054331 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A054331 <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 A054331 a(n) = 2^(2*n-3)*binomial(2*n+8, 7) = -A053125(n+7, 7)/8 = A054326(n)/8.
%F A054331 G.f. (1+4*x)*(1+24*x+16*x^2)/(1-4*x)^8.
%t A054331 Table[4^n Binomial[2n+8,7]/8,{n,0,20}] (* _Harvey P. Dale_, Nov 03 2011 *)
%t A054331 LinearRecurrence[{32,-448,3584,-17920,57344,-114688,131072,-65536},{1,60,1584,27456,366080,4073472,39690240,349274112},20] (* _Harvey P. Dale_, Feb 25 2022 *)
%o A054331 (PARI) vector(20, n, n--; 2^(2*n-3)*binomial(2*n+8, 7)) \\ _G. C. Greubel_, Jul 22 2019
%o A054331 (Magma) [2^(2*n-3)*Binomial(2*n+8, 7): n in [0..20]]; // _G. C. Greubel_, Jul 22 2019
%o A054331 (Sage) [2^(2*n-3)*binomial(2*n+8, 7) for n in (0..20)] # _G. C. Greubel_, Jul 22 2019
%o A054331 (GAP) List([0..20], n-> 2^(2*n-3)*Binomial(2*n+8, 7)); # _G. C. Greubel_, Jul 22 2019
%Y A054331 Cf. A054326, A053125.
%K A054331 easy,nice,nonn
%O A054331 0,2
%A A054331 _Wolfdieter Lang_