A054323 Fifth column of Lanczos triangle A053125 (decreasing powers).

5, 140, 2016, 21120, 183040, 1397760, 9748480, 63504384, 392232960, 2321285120, 13264486400, 73610035200, 398475657216, 2111580405760, 10984378859520, 56221121904640, 283661115064320, 1413061420253184, 6959221409054720

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 (20, -160, 640, -1280, 1024).

Formula

a(n) = 4^n*binomial(2*n+5, 4) = 4^n*A053126(n+4) = A053125(n+4, 4).

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

E.g.f.: (15 +360*x +1464*x^2 +1664*x^3 +512*x^4)*exp(4*x)/3. - G. C. Greubel, Jul 22 2019

a(n) = 20*a(n-1)-160*a(n-2)+640*a(n-3)-1280*a(n-4)+1024*a(n-5). - Wesley Ivan Hurt, May 02 2021

Mathematica

Table[4^n Binomial[2n+5, 4], {n, 0, 20}] (* or *) LinearRecurrence[{20, -160, 640, -1280, 1024}, {5, 140, 2016, 21120, 183040}, 20] (* Harvey P. Dale, Mar 03 2018 *)

Prog

(PARI) vector(20, n, n--; 4^n*binomial(2*n+5, 4)) \\ G. C. Greubel, Jul 22 2019
(Magma) [4^n*Binomial(2*n+5, 4): n in [0..20]]; // G. C. Greubel, Jul 22 2019
(Sage) [4^n*binomial(2*n+5, 4) for n in (0..20)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..20], n-> 4^n*Binomial(2*n+5, 4)); # G. C. Greubel, Jul 22 2019

Crossrefs

Cf. A053125, A054322.

Bisection of A080951.

Sequence in context: A279017 A091058 A155177 * A061320 A193756 A136464

Adjacent sequences: A054320 A054321 A054322 * A054324 A054325 A054326

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved