A054326 Eighth unsigned column of Lanczos triangle A053125 (decreasing powers).

8, 480, 12672, 219648, 2928640, 32587776, 317521920, 2794192896, 22682271744, 172438323200, 1241555927040, 8538764083200, 56469693136896, 361019918516224, 2240813287342080, 13550896696786944, 80073480481013760

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