A138334 C(n+11, 11)*(n+6)*(-1)^(n+1)*512/3.

-1024, 14336, -106496, 559104, -2329600, 8200192, -25346048, 70606848, -180590592, 429977600, -963149824, 2046693376, -4153583616, 8094162944, -15214592000, 27690557440, -48952949760, 84293314560, -141710499840, 233076480000

Offset: 0

Author

Klaus Brockhaus, Mar 15 2008

Keywords

• sign

Comments

Seventh column of the triangle defined in A123588, thirteenth column of the triangle defined in A123583.

Links

• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

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

Programs

Magma

[ Binomial(n+11, 11)*(n+6)*(-1)^(n+1)*512/3: n in [0..19] ];

Magma

k:=6; [ Coefficients(1-ChebyshevT(n+k)^2)[2*k+1]: n in [0..19] ];

Mathematica

Table[Binomial[n+11,11](n+6)(-1)^(n+1) 512/3,{n,0,20}] (* Harvey P. Dale, Jun 03 2021 *)

PARI

for(n=0,19,print1(polcoeff(taylor(1024*(x-1)/(x+1)^13,x),n),","));

Formula

a(n) = coefficient of x^12 in the polynomial 1 - T_(n+6)(x)^2, where T_n(x) is the n-th Chebyshev polynomial of the first kind.

G.f.: 1024*(x-1)/(x+1)^13.