Search: id:A053495
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%I A053495
%S A053495 1,1,1,1,2,2,1,4,6,6,1,6,18,24,24,1,9,36,96,120,120,1,
%T A053495 12,72,240,600,720,720,1,16,120,600,1800,4320,5040,5040,1,
%U A053495 20,200,1200,5400,15120,35280,40320,40320,1,25,300,2400,12600
%V A053495 1,1,-1,-1,2,-2,1,-4,6,-6,-1,6,-18,24,-24,1,-9,36,-96,120,-120,-1,
%W A053495 12,-72,240,-600,720,-720,1,-16,120,-600,1800,-4320,5040,-5040,-1,
%X A053495 20,-200,1200,-5400,15120,-35280,40320,-40320,1,-25,300,-2400,12600
%N 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,...}.
%F A053495 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}]
%F A053495 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]).
%e A053495 1, 1 - x, -1 + 2*x - 2*x^2, 1 - 4*x + 6*x^2 - 6*x^3, ...
%t A053495 CoefficientList[ #, x ]&/@Numerator[ FoldList[ (1/#1-x#2)&, 1, Range[ 
               12 ] ]//Together ]
%t A053495 FoldList[(1/#1-x#2)&, 1, Range[4] ]//Together (a simpler version, which 
               shows the rational functions)
%Y A053495 Diagonals give A000142, A001563, A001286, A001809, A001754, A001810, 
               A001755, A001811, A001777. Except for first term, row sums give negative 
               of A058307.
%Y A053495 Row sums of positive entries give A001053, those of negative entries 
               give -1*A001040.
%Y A053495 Sequence in context: A111062 A061598 A071946 this_sequence A096747 A167622 
               A084606
%Y A053495 Adjacent sequences: A053492 A053493 A053494 this_sequence A053496 A053497 
               A053498
%K A053495 sign,tabl,easy,nice
%O A053495 0,5
%A A053495 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jan 27 2001

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