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A054329
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One quarter of fourth unsigned column of Lanczos' triangle A053125.
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2
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1, 20, 224, 1920, 14080, 93184, 573440, 3342336, 18677760, 100925440, 530579456, 2726297600, 13740539904, 68115496960, 332859965440, 1606317768704, 7666516623360, 36232344109056, 169737107537920, 788899592929280
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OFFSET
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0,2
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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.: (1+4*x)/(1-4*x)^4.
E.g.f.: (3 + 48*x + 120*x^2 + 64*x^3)*exp(4*x)/3. - G. C. Greubel, Jul 22 2019
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MATHEMATICA
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Table[4^(n-1)*Binomial[2*n+4, 3], {n, 0, 30}] (* G. C. Greubel, Jul 22 2019 *)
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PROG
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(PARI) vector(30, n, n--; 4^(n-1)*binomial(2*n+4, 3)) \\ G. C. Greubel, Jul 22 2019
(Magma) [4^(n-1)*Binomial(2*n+4, 3): n in [0..30]]; // G. C. Greubel, Jul 22 2019
(Sage) [4^(n-1)*binomial(2*n+4, 3) for n in (0..30)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..30], n-> 4^(n-1)*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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