A054325 Seventh column of Lanczos triangle A053125 (decreasing powers).
7, 336, 7392, 109824, 1281280, 12673024, 111132672, 889061376, 6615662592, 46425702400, 310388981760, 1992378286080, 12352745373696, 74327630282752, 435713694760960, 2496217812566016, 14012859084177408, 77247357640507392
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 (28, -336, 2240, -8960, 21504, -28672, 16384).
Programs
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GAP
List([0..20], n-> 4^n*Binomial(2*n+7, 6)); # G. C. Greubel, Jul 22 2019
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Magma
[4^n*Binomial(2*n+7, 6): n in [0..20]]; // G. C. Greubel, Jul 22 2019
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Mathematica
Table[4^n*Binomial[2*n+7, 6], {n,0,20}] (* G. C. Greubel, Jul 22 2019 *) -
PARI
vector(20, n, n--; 4^n*binomial(2*n+7, 6)) \\ G. C. Greubel, Jul 22 2019
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Sage
[4^n*binomial(2*n+7, 6) for n in (0..20)] # G. C. Greubel, Jul 22 2019
Formula
a(n) = 4^n*binomial(2*n+7, 6) = A053125(n+6, 6).
G.f.: (7 +140*x +336*x^2 +64*x^3)/(1-4*x)^7.