A054327 Ninth column of Lanczos triangle A053125 (decreasing powers).
9, 660, 20592, 411840, 6223360, 77395968, 833495040, 8033304576, 70882099200, 581979340800, 4500640235520, 33087710822400, 232937484189696, 1579462143508480, 10363761453957120, 66060621396836352
Offset: 0
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).
Programs
-
GAP
List([0..20], 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
-
Mathematica
Table[4^n*Binomial[2*n+9, 8], {n,0,20}] (* G. C. Greubel, Jul 22 2019 *) -
PARI
vector(20, n, n--; 4^n*binomial(2*n+9,8)) \\ 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
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.