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

0,1

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A004017 A167471 A153115 * A290031 A008535 A008416

Adjacent sequences: A138328 A138329 A138330 * A138332 A138333 A138334

Keyword

sign,easy

Author

Klaus Brockhaus, Mar 15 2008

Status

approved