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 A158757 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. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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. REFERENCES H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973,page 221. LINKS FORMULA p(x,t)=Exp[t*x]/(1 - x^2/t^2 - t^3* x^3); with t^n*n! factor. EXAMPLE {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} MATHEMATICA 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}]; CROSSREFS Sequence in context: A193426 A156062 A156064 * A176917 A085983 A285701 Adjacent sequences:  A158754 A158755 A158756 * A158758 A158759 A158760 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 25 2009 STATUS approved

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