0,3

Row sums are are zero.

p(x,n) = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(2*m - 1)^ n*x^m, {m, 0, Infinity}]

- (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(2*m + 3)^n*x^m, {m, 0, Infinity}])/4;

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

{0},

{-1, 1},

{-2, 0, 2},

{-7, -3, 3, 7},

{-20, -56, 0, 56, 20},

{-61, -415, -370, 370, 415, 61},

{-182, -2632, -5710, 0, 5710, 2632, 182},

{-547, -15155, -64407, -49735, 49735, 64407, 15155, 547},

{-1640, -82896, -619696, -1085840, 0, 1085840, 619696, 82896, 1640},

{-4921, -439071, -5422116, -16914156, -11926446, 11926446, 16914156, 5422116, 439071, 4921},

{-14762, -2279024, -44560494, -224451744, -337197924, 0, 337197924, 224451744, 44560494, 2279024, 14762}

Clear[p]; p[x_, n_] = ((-1)^( n + 1)*(x - 1)^(n + 1)*Sum[(2*m - 1)^n*x^m, {m, 0, Infinity}]

- (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(2*m + 3)^n*x^m, {m, 0, Infinity}])/4;

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];

Flatten[%]

Sequence in context: A081081 A111111 A161014 this_sequence A088996 A021497 A029593

Adjacent sequences: A154849 A154850 A154851 this_sequence A154853 A154854 A154855

tabl,uned,tabl,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2009