A054329 One quarter of fourth unsigned column of Lanczos' triangle A053125.

1, 20, 224, 1920, 14080, 93184, 573440, 3342336, 18677760, 100925440, 530579456, 2726297600, 13740539904, 68115496960, 332859965440, 1606317768704, 7666516623360, 36232344109056, 169737107537920, 788899592929280

Offset

0,2

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 (16,-96,256,-256).

Formula

a(n)= 4^(n-1)*binomial(2*n+4, 3)= -A053125(n+3, 3)/4 = A054322(n)/4.

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

E.g.f.: (3 + 48*x + 120*x^2 + 64*x^3)*exp(4*x)/3. - G. C. Greubel, Jul 22 2019

Mathematica

Table[4^(n-1)*Binomial[2*n+4, 3], {n, 0, 30}] (* G. C. Greubel, Jul 22 2019 *)

Prog

(PARI) vector(30, n, n--; 4^(n-1)*binomial(2*n+4, 3)) \\ G. C. Greubel, Jul 22 2019
(Magma) [4^(n-1)*Binomial(2*n+4, 3): n in [0..30]]; // G. C. Greubel, Jul 22 2019
(Sage) [4^(n-1)*binomial(2*n+4, 3) for n in (0..30)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..30], n-> 4^(n-1)*Binomial(2*n+4, 3)); # G. C. Greubel, Jul 22 2019

Crossrefs

Cf. A054322, A053125.

Sequence in context: A000833 A302661 A178261 * A112503 A007160 A195265

Adjacent sequences: A054326 A054327 A054328 * A054330 A054331 A054332

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved