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

0,1

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A054324, A053125.

Sequence in context: A292336 A037116 A169996 * A024043 A199640 A221618

Adjacent sequences: A054327 A054328 A054329 * A054331 A054332 A054333

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved