A138331 a(n) = C(n+5, 5)*(n+3)*(-1)^(n+1)*16/3.

-16, 128, -560, 1792, -4704, 10752, -22176, 42240, -75504, 128128, -208208, 326144, -495040, 731136, -1054272, 1488384, -2062032, 2808960, -3768688, 4987136, -6517280, 8419840, -10764000, 13628160, -17100720, 21280896, -26279568, 32220160, -39239552

Offset: 0

Author

Klaus Brockhaus, Mar 15 2008

Keywords

• sign
• easy

Comments

Fourth column of the triangle defined in A123588, seventh column of the triangle defined in A123583.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (-7,-21,-35,-35,-21,-7,-1).

Crossrefs

Cf. A007318 (Pascal's triangle), A123588, A123583, A040977.

Programs

Magma

[ Binomial(n+5, 5)*(n+3)*(-1)^(n+1)*16/3: n in [0..28] ];

Magma

k:=3; [ Coefficients(1-ChebyshevT(n+k)^2)[2*k+1]: n in [0..28] ];

Maple

seq(binomial(n+5, 5)*(n+3)*(-1)^(n+1)*16/3, n=0..40); # Robert Israel, Oct 26 2017

Mathematica

LinearRecurrence[{-7,-21,-35,-35,-21,-7,-1},{-16,128,-560,1792,-4704,10752,-22176},30] (* Harvey P. Dale, May 27 2017 *)

PARI

for(n=0,28,print1(polcoeff(taylor(16*(x-1)/(x+1)^7,x),n),","));

Formula

a(n) = coefficient of x^6 in the polynomial 1 - T_(n+3)(x)^2, where T_n(x) is the n-th Chebyshev polynomial of the first kind.

G.f.: 16*(x-1)/(x+1)^7.

a(n) = (-1)^(n+1)*16*A040977(n).

a(n) = a(-n-5). - Bruno Berselli, Sep 13 2011