A002698 Coefficients of Chebyshev polynomials: n*(2*n-3)*2^(2*n-5). (Formerly M5059 N2189)

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

Offset

2,2

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

Table of n, a(n) for n=2..24.

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.

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)

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 *)

Crossrefs

Cf. A000079, A014107.

Sequence in context: A060932 A300078 A119004 * A222914 A171642 A158808

Adjacent sequences: A002695 A002696 A002697 * A002699 A002700 A002701

Keyword

nonn

Author

N. J. A. Sloane

Status

approved