A002698 Coefficients of Chebyshev polynomials: n*(2*n-3)*2^(2*n-5).

1, 18, 160, 1120, 6912, 39424, 212992, 1105920, 5570560, 27394048, 132120576, 627048448, 2936012800, 13589544960, 62277025792, 282930970624, 1275605286912, 5712306503680, 25426206392320, 112562502893568, 495879744126976, 2174833999740928, 9499780463984640

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

References

• Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 516.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Cornelius Lanczos, Applied Analysis. (Annotated scans of selected pages)
• Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
• Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
• Index entries for linear recurrences with constant coefficients, signature (12,-48,64).
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Cf. A000079, A014107.

Programs

Maple

A002698:=(-1-6*z+8*z**2)/(4*z-1)**3; # [Simon Plouffe in his 1992 dissertation]

Mathematica

Table[n*(2n-3)*2^(2n-5), {n, 2, 30}] (* Amiram Eldar, Feb 17 2023 *)

Formula

From Amiram Eldar, Feb 17 2023: (Start)

a(n) = A014107(n)*A000079(2*n-5).

Sum_{n>=2} 1/a(n) = 12*log(3) - 64*log(2)/3 + 8/3.

Sum_{n>=2} (-1)^n/a(n) = (8/3)*(arctan(1/2) + 4*log(5/4) - 1). (End)