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 A173293 Antidiagonal expansion of rational polynomial with factors: p(x,n) = If[n == 0, 1/(1 - x), x*ChebyshevU[n, x]/ChebyshevT[n + 1, x]]. 0
 1, 1, 0, 1, 0, 1, 1, -16, 0, 0, 1, 0, -24, 0, 1, 1, -128, 0, -256, 0, 0, 1, 0, -288, 0, -200, 0, 1, 1, -1024, 0, -24576, 0, -1296, 0, 0, 1, 0, -3456, 0, -12000, 0, -784, 0, 1, 1, -8192, 0, -2621440, 0, -590976, 0, -4096, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are {1, 1, 2, -15, -22, -383, -486, -26895, -16238, -3224703, ...}. The rational function here is associated with tan(n*arctan(x)). LINKS FORMULA p(x,n) = If[n == 0, 1/(1 - x), x*ChebyshevU[n, x]/ChebyshevT[n + 1, x]]; a(n,m) = (n+1)^m*expansion(p(x,n)); t(n,m) = antidiagonal(t(n,m)). EXAMPLE {1}, {1, 0}, {1, 0, 1}, {1, -16, 0, 0}, {1, 0, -24, 0, 1}, {1, -128, 0, -256, 0, 0}, {1, 0, -288, 0, -200, 0, 1}, {1, -1024, 0, -24576, 0, -1296, 0, 0}, {1, 0, -3456, 0, -12000, 0, -784, 0, 1}, {1, -8192, 0, -2621440, 0, -590976, 0, -4096, 0, 0} MATHEMATICA p[x_, n_] = If[n == 0, 1/(1 - x), x*ChebyshevU[n, x]/ChebyshevT[n + 1, x]]; a = Table[Table[(n + 1)^(m + 1)*SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], { m, 0, 20}], {n, 0, 20}]; Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]; Flatten[%] CROSSREFS Sequence in context: A306282 A169767 A225611 * A008433 A010111 A118067 Adjacent sequences:  A173290 A173291 A173292 * A173294 A173295 A173296 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 15 2010 STATUS approved

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Last modified June 4 07:42 EDT 2020. Contains 334822 sequences. (Running on oeis4.)