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A158706 A triangle sequence from a generating function polynomial: p(x,t) = exp(t*x)/(1 - x/t - t^2 * x^2); expanded over t. 0
1, 1, 0, 1, 2, 0, 2, 0, 3, 6, 0, 6, 0, 15, 0, 7, 24, 0, 24, 0, 84, 0, 52, 0, 37, 120, 0, 120, 0, 540, 0, 380, 0, 485, 0, 141, 720, 0, 720, 0, 3960, 0, 3000, 0, 5430, 0, 2406, 0, 1111, 5040, 0, 5040, 0, 32760, 0, 26040, 0, 60690, 0, 32802, 0, 28147, 0, 5923, 40320, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

FORMULA

p(x,t) = exp(t*x)/(1 - x/t - t^2* x^2); expanded over t.

EXAMPLE

{1},

{1, 0, 1},

{2, 0, 2, 0, 3},

{6, 0, 6, 0, 15, 0, 7},

{24, 0, 24, 0, 84, 0, 52, 0, 37},

{120, 0, 120, 0, 540, 0, 380, 0, 485, 0, 141},

{720, 0, 720, 0, 3960, 0, 3000, 0, 5430, 0, 2406, 0, 1111},

{5040, 0, 5040, 0, 32760, 0, 26040, 0, 60690, 0, 32802, 0, 28147, 0, 5923},

{40320, 0, 40320, 0, 302400, 0, 248640, 0, 707280, 0, 430416, 0, 529256, 0, 182120, 0, 62217},

{362880, 0, 362880, 0, 3084480, 0, 2600640, 0, 8724240, 0, 5748624, 0, 9132984, 0, 4000824, 0, 2586537, 0, 426457},

{3628800, 0, 3628800, 0, 34473600, 0, 29635200, 0, 114458400, 0, 79863840, 0, 154985040, 0, 78745680, 0, 73498410, 0, 20655370, 0, 5599531}

MATHEMATICA

Table[Expand[t^(n)*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x/t - t^2* x^2), \{x, 0, 20}], n]], {n, 0, 20}];

Table[CoefficientList[Expand[t^(n)*n!*SeriesCoefficient[Series[Exp[t*x]/( 1 - x/t - t^2* x^2), {x, 0, 20}], n]], t], {n, 0, 10}];

Flatten[%]

Table[Apply[ Plus, CoefficientList[Expand[t^( n)*n!*SeriesCoefficient[Series[Exp[t* x]/(1 - x/t - t^2* x^2), {x, 0, 20}], n]], t]], {n, 0, 10}];

CROSSREFS

Cf. A110313 (row sums).

Sequence in context: A242896 A240183 A112631 * A096500 A231563 A282849

Adjacent sequences:  A158703 A158704 A158705 * A158707 A158708 A158709

KEYWORD

nonn,tabf,uned

AUTHOR

Roger L. Bagula, Mar 24 2009

STATUS

approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)