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A138331
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C(n+5, 5)*(n+3)*(-1)^(n+1)*16/3.
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0
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-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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Fourth column of the triangle defined in A123588, seventh column of the triangle defined in A123583.
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
Index to sequences with linear recurrences with constant coefficients, signature (-7,-21,-35,-35,-21,-7,-1).
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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
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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), ", "));
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CROSSREFS
| Cf. A007318 (Pascal's triangle), A123588, A123583, A040977.
Sequence in context: A004017 A167471 A153115 * A008535 A008416 A045651
Adjacent sequences: A138328 A138329 A138330 * A138332 A138333 A138334
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KEYWORD
| sign,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 15 2008
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