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 A053495 Triangle formed by coefficients of numerator polynomials defined by iterating f(u,v) = 1/u - x*v applied to a list of elements {1,2,3,4,...}. 22
 1, 1, -1, -1, 2, -2, 1, -4, 6, -6, -1, 6, -18, 24, -24, 1, -9, 36, -96, 120, -120, -1, 12, -72, 240, -600, 720, -720, 1, -16, 120, -600, 1800, -4320, 5040, -5040, -1, 20, -200, 1200, -5400, 15120, -35280, 40320, -40320, 1, -25, 300, -2400, 12600 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS FORMULA Table[ (-1)^(r+c+1) binomial[Floor[(r+c)/2], Floor[(r-c)/2]] Floor[(r+c+1)/2]! / Floor[(r-c+1)/2]!, {r, 0, 7}, {c, 0, r}] a[0] := -1; a[1] := 1-x; a[n_] := a[n]= n x a[n-1] + a[n-2] (matches sequence except for a[0]). EXAMPLE 1, 1 - x, -1 + 2*x - 2*x^2, 1 - 4*x + 6*x^2 - 6*x^3, ... MATHEMATICA CoefficientList[ #, x ]&/@Numerator[ FoldList[ (1/#1-x#2)&, 1, Range[ 12 ] ]//Together ] FoldList[(1/#1-x#2)&, 1, Range[4] ]//Together (a simpler version, which shows the rational functions) CROSSREFS Diagonals give A000142, A001563, A001286, A001809, A001754, A001810, A001755, A001811, A001777. Except for first term, row sums give negative of A058307. Row sums of positive entries give A001053, those of negative entries give -1*A001040. Sequence in context: A191490 A061598 A071946 * A096747 A299504 A300979 Adjacent sequences:  A053492 A053493 A053494 * A053496 A053497 A053498 KEYWORD sign,tabl,easy,nice AUTHOR Wouter Meeussen, Jan 27 2001 STATUS approved

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)