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A158757
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Expansion in t of generating function: p(x,t)=Exp[t*x]/(1 - x^2/t^2 - t^3* x^3); with t^n*n! factor.
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0
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1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 7, 24, 0, 0, 0, 12, 0, 0, 0, 25, 0, 0, 120, 0, 0, 0, 260, 0, 0, 0, 61, 720, 0, 0, 0, 360, 0, 0, 0, 1470, 0, 0, 0, 841, 0, 0, 5040, 0, 0, 0, 15960, 0, 0, 0, 5082, 0, 0, 0, 5251, 40320, 0, 0, 0, 20160, 0, 0, 0, 122640, 0, 0, 0, 134456, 0, 0, 0
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OFFSET
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0,5
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COMMENTS
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Row sums are:
{1, 1, 3, 13, 61, 441, 3391, 31333, 338073, 3965041, 52986331,...}.
Padovan/ minimal Pisot {3,3,5} as cubic 600 cell type polynomial.
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REFERENCES
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H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973,page 221.
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LINKS
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Table of n, a(n) for n=0..79.
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FORMULA
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p(x,t)=Exp[t*x]/(1 - x^2/t^2 - t^3* x^3); with t^n*n! factor.
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EXAMPLE
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{1},
{0, 0, 1},
{2, 0, 0, 0, 1},
{0, 0, 6, 0, 0, 0, 7},
{24, 0, 0, 0, 12, 0, 0, 0, 25},
{0, 0, 120, 0, 0, 0, 260, 0, 0, 0, 61},
{720, 0, 0, 0, 360, 0, 0, 0, 1470, 0, 0, 0, 841},
{0, 0, 5040, 0, 0, 0, 15960, 0, 0, 0, 5082, 0, 0, 0, 5251},
{40320, 0, 0, 0, 20160, 0, 0, 0, 122640, 0, 0, 0, 134456, 0, 0, 0, 20497},
{0, 0, 362880, 0, 0, 0, 1512000, 0, 0, 0, 547344, 0, 0, 0, 1118952, 0, 0, 0, 423865},
{3628800, 0, 0, 0, 1814400, 0, 0, 0, 14666400, 0, 0, 0, 23592240, 0, 0, 0, 5503770, 0, 0, 0, 3780721}
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MATHEMATICA
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Table[Expand[t^n*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x^2/t^2 - t^3* x^3), {x, 0, 20}], n]], {n, 0, 10}];
Table[CoefficientList[Expand[t^n*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x^2/t^2 - t^3* x^3), {x, 0, 20}], n]], t], {n, 0, 10}];
Flatten[%]
Table[Apply[ Plus, CoefficientList[Expand[ t^n*n!*SeriesCoefficient[Series[Exp[ t*x]/(1 - x^2/t^2 - t^3* x^3), {x, 0, 20}], n]], t]], {n, 0, 10}];
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CROSSREFS
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Sequence in context: A193426 A156062 A156064 * A176917 A085983 A088183
Adjacent sequences: A158754 A158755 A158756 * A158758 A158759 A158760
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Mar 25 2009
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STATUS
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approved
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