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A054327 Ninth column of Lanczos triangle A053125 (decreasing powers). 2
9, 660, 20592, 411840, 6223360, 77395968, 833495040, 8033304576, 70882099200, 581979340800, 4500640235520, 33087710822400, 232937484189696, 1579462143508480, 10363761453957120, 66060621396836352 (list; graph; refs; listen; history; text; internal format)
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 (36, -576, 5376, -32256, 129024, -344064, 589824, -589824, 262144).

FORMULA

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.

MATHEMATICA

Table[4^n*Binomial[2*n+9, 8], {n, 0, 20}] (* G. C. Greubel, Jul 22 2019 *)

PROG

(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

CROSSREFS

Cf. A053125, A054326.

Sequence in context: A091062 A221133 A015007 * A209964 A287937 A053973

Adjacent sequences:  A054324 A054325 A054326 * A054328 A054329 A054330

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified October 20 05:42 EDT 2019. Contains 328247 sequences. (Running on oeis4.)