A054324 Sixth unsigned column of Lanczos triangle A053125 (decreasing powers).
6, 224, 4032, 50688, 512512, 4472832, 35094528, 254017536, 1725825024, 11142168576, 68975329280, 412216197120, 2390853943296, 13514114596864, 74693776244736, 404792077713408, 2155824474488832, 11304491362025472
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
- G. C. Greubel, 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 (24, -240, 1280, -3840, 6144, -4096).
Programs
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GAP
List([0..20], n-> 4^n*Binomial(2*n+6, 5)); # G. C. Greubel, Jul 22 2019
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Magma
[4^n*Binomial(2*n+6, 5): n in [0..20]]; // G. C. Greubel, Jul 22 2019
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Mathematica
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 *) -
PARI
vector(20, n, n--; 4^n*binomial(2*n+6, 5)) \\ G. C. Greubel, Jul 22 2019
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Sage
[4^n*binomial(2*n+6, 5) for n in (0..20)] # G. C. Greubel, Jul 22 2019
Formula
G.f.: 2*(3+4*x)*(1+12*x)/(1-4*x)^6.
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