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 A155994 A triangle of polynomial coefficients: p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n)); sp(x,n) = p(x, n) + x^n*p(1/x, n). 0
 -2, -3, 8, -3, -6, 10, 10, -6, -17, 16, 24, 16, -17, -30, 4, 52, 52, 4, -30, -63, 24, 56, 80, 56, 24, -63, -126, 22, 234, -10, -10, 234, 22, -126, -257, 32, 488, 224, -480, 224, 488, 32, -257, -510, 8, 1096, 328, -420, -420, 328, 1096, 8, -510, -1023, 40, 2244, 480 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are: {-2, 0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026,...}. LINKS FORMULA p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n)); sp(x,n) = p(x, n) + x^n*p(1/x, n). EXAMPLE {-2}, {}, {-3, 8, -3}, {-6, 10, 10, -6}, {-17, 16, 24, 16, -17}, {-30, 4, 52, 52, 4, -30}, {-63, 24, 56, 80, 56, 24, -63}, {-126, 22, 234, -10, -10, 234, 22, -126}, {-257, 32, 488, 224, -480, 224, 488, 32, -257}, {-510, 8, 1096, 328, -420, -420, 328, 1096, 8, -510}, {-1023, 40, 2244, 480, -1232, 1008, -1232, 480, 2244, 40, -1023} MATHEMATICA p[x_, n_] =-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n)); sp[x_, n_] = p[x, n] + x^n*p[1/x, n]; Table[FullSimplify[ExpandAll[sp[x, n]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[sp[x, n]]], x], {n, 0, 10}]; Q Flatten[%] CROSSREFS Sequence in context: A183168 A011326 A154826 * A011162 A293273 A079555 Adjacent sequences:  A155991 A155992 A155993 * A155995 A155996 A155997 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 01 2009 STATUS approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)