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A054322
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Fourth unsigned column of Lanczos triangleA053125(decreasing powers).
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3
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4, 80, 896, 7680, 56320, 372736, 2293760, 13369344, 74711040, 403701760, 2122317824, 10905190400, 54962159616, 272461987840, 1331439861760, 6425271074816, 30666066493440, 144929376436224, 678948430151680
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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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G.f.: 4*(1+4*x)/(1-4*x)^4.
E.g.f.: (4/3)*(3 +48*x +120*x^2 +64*x^3)*exp(4*x). -G. C. Greubel,Jul 22 2019
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MATHEMATICA
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Table[4^n*Binomial[2*n+4, 3], {n, 0, 20}] (*G. C. Greubel,Jul 22 2019 *)
LinearRecurrence[{16, -96, 256, -256}, {4, 80, 896, 7680}, 20] (*Harvey P. Dale,Mar 27 2023 *)
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PROG
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(PARI) vector(20, n, n--; 4^n*binomial(2*n+4, 3)) \\G. C. Greubel,Jul 22 2019
(Magma) [4^n*Binomial(2*n+4, 3): n in [0..20]]; //G. C. Greubel,Jul 22 2019
(Sage) [4^n*binomial(2*n+4, 3) for n in (0..20)] #G. C. Greubel,Jul 22 2019
(GAP) List([0..20], n-> 4^n*Binomial(2*n+4, 3)); #G. C. Greubel,Jul 22 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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