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 A174986 Numerator coefficients of an infinite sum polynomial:p(x,n)=Sum[(((1 + Sqrt[5])^k - (1 - Sqrt[5])^k)/(2^k* Sqrt[5]))^n*x^k, {k, 0, Infinity}] 0
 -2, -1, 1, 5, -10, -5, -2, 8, 8, -2, -10, 70, 160, -70, -10, -1, 12, 53, -53, -12, 1, 20, -400, -3320, 6360, 3320, -400, -20, -2, 66, 984, -3568, -3568, 984, 66, -2, -10, 540, 14130, -92880, -178400, 92880, 14130, -540, -10, -4, 352, 15840, -184932, -654016 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are: {-2, 0, -10, 12, 140, 0, 5560, -5040, -150160, 0,...}. The result seems to be a beta integer version of a Eulerian infinite sum. LINKS FORMULA p(x,n)=Sum[(((1 + Sqrt[5])^k - (1 - Sqrt[5])^k)/(2^k* Sqrt[5]))^n*x^k, {k, 0, Infinity}] out_n,m=Numerator_coefficients(p(x,n)/x)/2^(1 + Floor[n/2]) EXAMPLE {-2}, {-1, 1}, {5, -10, -5}, {-2, 8, 8, -2}, {-10, 70, 160, -70, -10}, {-1, 12, 53, -53, -12, 1}, {20, -400, -3320, 6360, 3320, -400, -20}, {-2, 66, 984, -3568, -3568, 984, 66, -2}, {-10, 540, 14130, -92880, -178400, 92880, 14130, -540, -10}, {-4, 352, 15840, -184932, -654016, 654016, 184932, -15840, -352, 4} MATHEMATICA p[x_, n_] = Sum[(((1 + Sqrt[5])^k - (1 - Sqrt[5])^k)/(2^k*Sqrt[5]))^n*x^k, {k, 0, Infinity}]; Flatten[Table[CoefficientList[FullSimplify[Numerator[p[x, n]]/x], x]/2^(1 + Floor[n/2]), {n, 1, 10}]] CROSSREFS Sequence in context: A098315 A006704 A324960 * A327671 A036563 A025264 Adjacent sequences:  A174983 A174984 A174985 * A174987 A174988 A174989 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 03 2010 STATUS approved

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Last modified June 15 02:56 EDT 2021. Contains 345042 sequences. (Running on oeis4.)