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%I #12 Feb 18 2024 05:10:38
%S 2,2,8,0,2,48,0,6,384,0,32,0,-10,3840,0,240,0,-110,46080,0,2304,0,
%T -1368,0,21,645120,0,26880,0,-19488,0,448,10321920,0,368640,0,-314880,
%U 0,8992,0,-32,185794560,0,5806080,0,-5702400,0,186912,0,-1152,3715891200,0,103219200,0,-114508800,0,4131840,0,-34280,0,46
%N Triangle: No(x, n) = (2*n/x)*No(x, n - 1) + (-n/(n - 2))*No( x, n - 2) + Ceiling[(2*(n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x; weighted by 2*x^(n + 1).
%e {2},
%e {2},
%e {8, 0, 2},
%e {48, 0, 6},
%e {384, 0, 32, 0, -10},
%e {3840, 0, 240, 0, -110},
%e {46080, 0, 2304, 0, -1368, 0, 21},
%e {645120, 0, 26880, 0, -19488,0, 448},
%e {10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32},
%e {185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152},
%e {3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46}
%e ...
%t No[x, -1] = 0;
%t No[x, 0] = 1/x;
%t No[x, 1] = 1/x^2;
%t No[x, 2] = (x^2 + 4)/x^3;
%t No[x_, n_] := No[x, n] = (2*n/x)*No[ x, n - 1] + (-n/(n - 2))*No[x, n - 2] + Ceiling[(2*( n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x;
%t Table[ExpandAll[2*x^(n + 1)*No[x, n]], {n, 0, 10}];
%t a = Table[CoefficientList[2*x^(n + 1)*No[x, n], x], {n, 0, 10}];
%t Flatten[a]
%K uned,tabf,sign,less
%O 1,1
%A _Roger L. Bagula_, Apr 09 2008
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