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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
2, 2, 8, 0, 2, 48, 0, 6, 384, 0, 32, 0, -10, 3840, 0, 240, 0, -110, 46080, 0, 2304, 0, -1368, 0, 21, 645120, 0, 26880, 0, -19488, 0, 448, 10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32, 185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152, 3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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).

EXAMPLE

{2},

{2},

{8, 0, 2},

{48, 0, 6},

{384, 0, 32, 0, -10},

{3840, 0, 240, 0, -110},

{46080, 0, 2304, 0, -1368, 0, 21},

{645120, 0, 26880, 0, -19488,0, 448},

{10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32},

{185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152},

{3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46}

MATHEMATICA

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]

CROSSREFS

Sequence in context: A248237 A139523 A079242 * A051148 A102645 A037300

Adjacent sequences:  A137381 A137382 A137383 * A137385 A137386 A137387

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Apr 09 2008

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)