A054328 Tenth unsigned column of Lanczos triangle A053125 (decreasing powers).

10, 880, 32032, 732160, 12446720, 171991040, 2037432320, 21422145536, 204770508800, 1810602393600, 15002134118400, 117645194035200, 879986051383296, 6317848574033920, 43758103916707840, 293602761763717120, 1915090741504245760, 12179333387986665472, 75709369709106298880

Offset

0,1

References

Cornelius Lanczos, Applied Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.

Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2nd ed., Wiley, New York, 1990.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (40,-720,7680,-53760,258048,-860160,1966080,-2949120, 2621440,-1048576).

Index entries for sequences related to Chebyshev polynomials.

Formula

a(n) = 4^n*binomial(2*n+10, 9)= -A053125(n+9, 9) = 2* A054332(n).

G.f. 2*(1+40*x+80*x^2)*(5+40*x+16*x^2)/(1-4*x)^10.

From Amiram Eldar, Oct 30 2025: (Start)

Sum_{n>=0} 1/a(n) = 3351057/70 + 118116*log(2) - 118098*log(3).

Sum_{n>=0} (-1)^n/a(n) = -244401/70 + 12096*arctan(1/2) - 9486*log(5/4). (End)

Mathematica

CoefficientList[Series[2(1+40x+80x^2)(5+40x+16x^2)/(1-4x)^10, {x, 0, 20}], x]  (* Harvey P. Dale, Feb 28 2011 *)
Table[4^n*Binomial[2*n+10, 9], {n, 0, 20}] (* G. C. Greubel, Jul 22 2019 *)

Prog

(PARI) vector(20, n, n--; 4^n*binomial(2*n+10, 9)) \\ G. C. Greubel, Jul 22 2019
(Magma) [4^n*Binomial(2*n+10, 9): n in [0..20]]; // G. C. Greubel, Jul 22 2019
(SageMath) [4^n*binomial(2*n+10, 9) for n in (0..20)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..20], n-> 4^n*Binomial(2*n+10, 9)); # G. C. Greubel, Jul 22 2019

Crossrefs

Cf. A053125, A054327, A054332.

Sequence in context: A015033 A126677 A370223 * A203590 A263056 A233125

Adjacent sequences: A054325 A054326 A054327 * A054329 A054330 A054331

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved