A002698 - OEIS

%I M5059 N2189 #42 Oct 19 2023 08:25:44

%S 1,18,160,1120,6912,39424,212992,1105920,5570560,27394048,132120576,

%T 627048448,2936012800,13589544960,62277025792,282930970624,

%U 1275605286912,5712306503680,25426206392320,112562502893568,495879744126976,2174833999740928,9499780463984640

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

%D Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 516.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Cornelius Lanczos, <a href="/A002457/a002457.pdf">Applied Analysis</a>. (Annotated scans of selected pages)

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-48,64).

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.

%F From _Amiram Eldar_, Feb 17 2023: (Start)

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

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

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

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

%t Table[n*(2n-3)*2^(2n-5), {n, 2, 30}] (* _Amiram Eldar_, Feb 17 2023 *)

%Y Cf. A000079, A014107.

%K nonn

%O 2,2

%A _N. J. A. Sloane_