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A054327 Ninth column of Lanczos triangle A053125 (decreasing powers). 2
9, 660, 20592, 411840, 6223360, 77395968, 833495040, 8033304576, 70882099200, 581979340800, 4500640235520, 33087710822400, 232937484189696, 1579462143508480, 10363761453957120, 66060621396836352 (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
Index entries for linear recurrences with constant coefficients, signature (36, -576, 5376, -32256, 129024, -344064, 589824, -589824, 262144).
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.
MATHEMATICA
Table[4^n*Binomial[2*n+9, 8], {n, 0, 20}] (* G. C. Greubel, Jul 22 2019 *)
PROG
(PARI) vector(20, n, 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
(Sage) [4^n*binomial(2*n+9, 8) for n in (0..20)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..20], n-> 4^n*Binomial(2*n+9, 8)); # G. C. Greubel, Jul 22 2019
CROSSREFS
Sequence in context: A091062 A221133 A015007 * A209964 A287937 A053973
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 25 06:42 EDT 2024. Contains 371964 sequences. (Running on oeis4.)