A054330 One half of sixth unsigned column of Lanczos' triangle A053125.

3, 112, 2016, 25344, 256256, 2236416, 17547264, 127008768, 862912512, 5571084288, 34487664640, 206108098560, 1195426971648, 6757057298432, 37346888122368, 202396038856704, 1077912237244416, 5652245681012736

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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 (24, -240, 1280, -3840, 6144, -4096).

Crossrefs

Cf. A054324, A053125.

Programs

GAP

List([0..20], n-> 2^(2*n-1)*Binomial(2*n+6,5)); # G. C. Greubel, Jul 22 2019

Magma

[2^(2*n-1)*Binomial(2*n+6,5): n in [0..20]]; // G. C. Greubel, Jul 22 2019

Mathematica

Table[2^(2*n-1)*Binomial[2*n+6, 5], {n,0,20}] (* G. C. Greubel, Jul 22 2019 *)

PARI

vector(20, n, n--; 2^(2*n-1)*binomial(2*n+6,5)) \\ G. C. Greubel, Jul 22 2019

Sage

[2^(2*n-1)*binomial(2*n+6,5) for n in (0..20)] # G. C. Greubel, Jul 22 2019

Formula

a(n)= 2^(2*n-1)*binomial(2*n+6, 5) = -A053125(n+5, 5)/2 = A054324(n)/2.

G.f.: (4*x+3)*(12*x+1)/(1-4*x)^6.

E.g.f.: (90 + 3000*x + 17520*x^2 + 31680*x^3 + 20480*x^4 + 4096*x^5)* exp(4*x)/30. - G. C. Greubel, Jul 22 2019