login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 15:32 EST 2016. Contains 279003 sequences.