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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

Table of n, a(n) for n=0..79.

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 A088183

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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Last modified November 27 01:09 EST 2014. Contains 250152 sequences.