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A138331
a(n) = C(n+5, 5)*(n+3)*(-1)^(n+1)*16/3.
1
-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.
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
KEYWORD
sign,easy
AUTHOR
Klaus Brockhaus, Mar 15 2008
STATUS
approved