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 A137384 A triangular sequence of coefficients of a modified Neumann polynomial recursion: 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). 0

%I

%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 A triangular sequence of coefficients of a modified Neumann polynomial recursion: 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).

%C Row sums are: {2, 2, 10, 54, 406, 3970, 47037, 652960, 10384640, 186084000, 3708699206};

%C The ceiling function and 2*x^(n+1) were used to give integers.

%D Weisstein, Eric W. "Neumann Polynomial." http://mathworld.wolfram.com/NeumannPolynomial.html

%F 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}

%t Clear[No, a] No[x, -1] = 0; No[x, 0] = 1/x; No[x, 1] = 1/x^2; No[x, 2] = (x^2 + 4)/x^3; 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; Table[ExpandAll[2*x^(n + 1)*No[x, n]], {n, 0, 10}]; a = Table[CoefficientList[2*x^(n + 1)*No[x, n], x], {n, 0, 10}]; Flatten[a]

%K uned,tabl,sign

%O 1,1

%A _Roger L. Bagula_, Apr 09 2008

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Last modified July 22 06:22 EDT 2019. Contains 325213 sequences. (Running on oeis4.)