A054322 Fourth unsigned column of Lanczos triangle A053125 (decreasing powers).

4, 80, 896, 7680, 56320, 372736, 2293760, 13369344, 74711040, 403701760, 2122317824, 10905190400, 54962159616, 272461987840, 1331439861760, 6425271074816, 30666066493440, 144929376436224, 678948430151680

Offset

0,1

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 (16,-96,256,-256).

Formula

a(n) = 4^n*binomial(2*n+4, 3) = -A053125(n+3, 3) = 4*A054329(n).

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A053125, A053123, A002700, A054329.

Sequence in context: A366955 A269146 A192834 * A114488 A055787 A132584

Adjacent sequences: A054319 A054320 A054321 * A054323 A054324 A054325

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved