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A054327
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Ninth column of Lanczos triangle A053125 (decreasing powers).
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2
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9, 660, 20592, 411840, 6223360, 77395968, 833495040, 8033304576, 70882099200, 581979340800, 4500640235520, 33087710822400, 232937484189696, 1579462143508480, 10363761453957120, 66060621396836352
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OFFSET
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0,1
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REFERENCES
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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.
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LINKS
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FORMULA
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a(n) = 4^n*binomial(2*n+9, 8) = A053125(n+8, 8).
G.f.: (4*x+3)*(64*x^3+528*x^2+108*x+3)/(1-4*x)^9.
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MATHEMATICA
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Table[4^n*Binomial[2*n+9, 8], {n, 0, 20}] (* G. C. Greubel, Jul 22 2019 *)
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PROG
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(PARI) vector(20, n, n--; 4^n*binomial(2*n+9, 8)) \\ G. C. Greubel, Jul 22 2019
(Magma) [4^n*Binomial(2*n+9, 8): n in [0..20]]; // G. C. Greubel, Jul 22 2019
(Sage) [4^n*binomial(2*n+9, 8) for n in (0..20)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..20], n-> 4^n*Binomial(2*n+9, 8)); # G. C. Greubel, Jul 22 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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