A054326 Eighth unsigned column of Lanczos triangle A053125 (decreasing powers).
8, 480, 12672, 219648, 2928640, 32587776, 317521920, 2794192896, 22682271744, 172438323200, 1241555927040, 8538764083200, 56469693136896, 361019918516224, 2240813287342080, 13550896696786944, 80073480481013760
Offset: 0
References
- C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
- Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for sequences related to Chebyshev polynomials.
- Index entries for linear recurrences with constant coefficients, signature (32, -448, 3584, -17920, 57344, -114688, 131072, -65536).
Programs
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GAP
List([0..20], n-> 4^n*Binomial(2*n+8,7)); # G. C. Greubel, Jul 22 2019
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Magma
[4^n*Binomial(2*n+8,7): n in [0..20]]; // G. C. Greubel, Jul 22 2019
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Mathematica
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 *) -
PARI
vector(20, n, n--; 4^n*binomial(2*n+8,7)) \\ G. C. Greubel, Jul 22 2019
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Sage
[4^n*binomial(2*n+8,7) for n in (0..20)] # G. C. Greubel, Jul 22 2019
Formula
G.f.: 8*(4*x+1)*(16*x^2+24*x+1)/(1-4*x)^8.
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