0,5

Row sums are:

A110313;

{1, 2, 7, 34, 221, 1786, 17347, 196442, 2542969, 37030546, 599172671,

10664259442, 207061905877, 4355429249354, 98661276360571, 2394559287772906,

61991654930903537, 1705178260099590562, 49662655090649112439,

1526761411676393108546, 49407037167974524897741,...}.

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

{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}

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}];

A110313

Sequence in context: A136166 A046522 A112631 this_sequence A096500 A111813 A167156

Adjacent sequences: A158703 A158704 A158705 this_sequence A158707 A158708 A158709

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 24 2009