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A054326 Eighth unsigned column of Lanczos triangle A053125 (decreasing powers). 3
8, 480, 12672, 219648, 2928640, 32587776, 317521920, 2794192896, 22682271744, 172438323200, 1241555927040, 8538764083200, 56469693136896, 361019918516224, 2240813287342080, 13550896696786944, 80073480481013760 (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

Harvey P. Dale, 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 (32, -448, 3584, -17920, 57344, -114688, 131072, -65536).

FORMULA

a(n) = 4^n*binomial(2*n+8, 7) = -A053125(n+7, 7) = 8*A054331(n).

G.f.: 8*(4*x+1)*(16*x^2+24*x+1)/(1-4*x)^8.

a(0)=8, a(1)=480, a(2)=12672, a(3)=219648, a(4)=2928640, a(5)=32587776, a(6)=317521920, a(7)=2794192896, a(n) = 32*a(n-1) - 448*a(n-2) + 3584*a(n-3) - 17920*a(n-4) + 57344*a(n-5) - 114688*a(n-6) + 131072*a(n-7) - 65536*a(n-8). - Harvey P. Dale, Oct 23 2012

MATHEMATICA

Table[4^n Binomial[2n+8, 7], {n, 0, 20}] (* or *) LinearRecurrence[{32, -448, 3584, -17920, 57344, -114688, 131072, -65536}, {8, 480, 12672, 219648, 2928640, 32587776, 317521920, 2794192896}, 20] (* Harvey P. Dale, Oct 23 2012 *)

PROG

(PARI) vector(20, n, n--; 4^n*binomial(2*n+8, 7)) \\ G. C. Greubel, Jul 22 2019

(MAGMA) [4^n*Binomial(2*n+8, 7): n in [0..20]]; // G. C. Greubel, Jul 22 2019

(Sage) [4^n*binomial(2*n+8, 7) for n in (0..20)] # G. C. Greubel, Jul 22 2019

(GAP) List([0..20], n-> 4^n*Binomial(2*n+8, 7)); # G. C. Greubel, Jul 22 2019

CROSSREFS

Cf. A053125, A054325, A054331.

Sequence in context: A221157 A015006 A279383 * A203526 A210117 A204564

Adjacent sequences:  A054323 A054324 A054325 * A054327 A054328 A054329

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)