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A138334
C(n+11, 11)*(n+6)*(-1)^(n+1)*512/3.
0
-1024, 14336, -106496, 559104, -2329600, 8200192, -25346048, 70606848, -180590592, 429977600, -963149824, 2046693376, -4153583616, 8094162944, -15214592000, 27690557440, -48952949760, 84293314560, -141710499840, 233076480000
OFFSET
0,1
COMMENTS
Seventh column of the triangle defined in A123588, thirteenth column of the triangle defined in A123583.
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.
MATHEMATICA
Table[Binomial[n+11, 11](n+6)(-1)^(n+1) 512/3, {n, 0, 20}] (* Harvey P. Dale, Jun 03 2021 *)
PROG
(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] ];
(PARI) for(n=0, 19, print1(polcoeff(taylor(1024*(x-1)/(x+1)^13, x), n), ", "));
CROSSREFS
Cf. A007318 (Pascal's triangle), A123588, A123583.
Sequence in context: A197909 A218526 A221488 * A268124 A205611 A016781
KEYWORD
sign
AUTHOR
Klaus Brockhaus, Mar 15 2008
STATUS
approved