0,5

Row sums are:

{1, 2, 5, 16, 89, 686, 5917, 54860, 588401, 7370074, 103522421,...}.

Last column is:

{1, 1, 1, 1, 25, 121, 361, 841, 42001, 365905, 1819441,...}.

First column is n!.

With weighting factors t^n*n!;

p(x,t)=Exp[t*x]/(1 - x/t - t^4* x^4);

t(n,m)=coefficients(expansion(p(x,t),t),t).

{1},

{1, 0, 1},

{2, 0, 2, 0, 1},

{6, 0, 6, 0, 3, 0, 1},

{24, 0, 24, 0, 12, 0, 4, 0, 25},

{120, 0, 120, 0, 60, 0, 20, 0, 245, 0, 121},

{720, 0, 720, 0, 360, 0, 120, 0, 2190, 0, 1446, 0, 361},

{5040, 0, 5040, 0, 2520, 0, 840, 0, 20370, 0, 15162, 0, 5047, 0, 841},

{40320, 0, 40320, 0, 20160, 0, 6720, 0, 203280, 0, 161616, 0, 60536, 0, 13448, 0, 42001},

{362880, 0, 362880, 0, 181440, 0, 60480, 0, 2192400, 0, 1817424, 0, 726264, 0, 181512, 0, 1118889, 0, 365905},

{3628800, 0, 3628800, 0, 1814400, 0, 604800, 0, 25552800, 0, 21803040, 0, 9077040, 0, 2419920, 0, 22226490, 0, 10946890, 0, 1819441}

Table[Expand[t^(n)*n!*SeriesCoefficient[Series[Exp[t*x]/(1 - x/t - t^4* x^4), {x, 0, 20}], n]], {n, 0, 10}];

a = Table[CoefficientList[Expand[t^(n)*n!*SeriesCoefficient[Series[Exp[t* x]/(1 - x/t - t^4* x^4), {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^4* x^4), {x, 0, 20}], n]], t]], {n, 0, 10}];

Sequence in context: A064984 A038555 A138108 this_sequence A039970 A105118 A103271

Adjacent sequences: A158774 A158775 A158776 this_sequence A158778 A158779 A158780

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 26 2009