A054331 One eighth of eighth unsigned column of Lanczos' triangle A053125.

1, 60, 1584, 27456, 366080, 4073472, 39690240, 349274112, 2835283968, 21554790400, 155194490880, 1067345510400, 7058711642112, 45127489814528, 280101660917760, 1693862087098368, 10009185060126720, 57935518230380544

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 (32,-448,3584,-17920,57344,-114688,131072,-65536).

Formula

a(n) = 2^(2*n-3)*binomial(2*n+8, 7) = -A053125(n+7, 7)/8 = A054326(n)/8.

G.f. (1+4*x)*(1+24*x+16*x^2)/(1-4*x)^8.

Mathematica

Table[4^n Binomial[2n+8, 7]/8, {n, 0, 20}] (* Harvey P. Dale, Nov 03 2011 *)
LinearRecurrence[{32, -448, 3584, -17920, 57344, -114688, 131072, -65536}, {1, 60, 1584, 27456, 366080, 4073472, 39690240, 349274112}, 20] (* Harvey P. Dale, Feb 25 2022 *)

Prog

(PARI) vector(20, n, n--; 2^(2*n-3)*binomial(2*n+8, 7)) \\ G. C. Greubel, Jul 22 2019
(Magma) [2^(2*n-3)*Binomial(2*n+8, 7): n in [0..20]]; // G. C. Greubel, Jul 22 2019
(Sage) [2^(2*n-3)*binomial(2*n+8, 7) for n in (0..20)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..20], n-> 2^(2*n-3)*Binomial(2*n+8, 7)); # G. C. Greubel, Jul 22 2019

Crossrefs

Cf. A054326, A053125.

Sequence in context: A289156 A288960 A269196 * A160349 A281373 A053528

Adjacent sequences: A054328 A054329 A054330 * A054332 A054333 A054334

Keyword

easy,nice,nonn

Author

Wolfdieter Lang

Status

approved