0,1

Row sums are:

{2, -2, 6, -30, 210, -1890, 20790, -270270, 4054050, -68918850, 1309458150,...}.

The Stirling product form is: as even- odd factorization;

Product[x-i,{i,0,n}]=Product[x-(2*i),{i,0,Floor[n/2]}]*Product[x-(2*i+1),{i,0,Floor[n/2]}]

p(x,n)=Product[x - (2*i), {i, 0, Floor[n/2]}]/x;

t(n,m)=coefficients(p(x,n)+x^n*p(1/x,n));

t(n,m)=A039683(n,m)+A039683(n,n-m).

{2},

{-1, -1},

{9, -12, 9},

{-47, 32, 32, -47},

{385, -420, 280, -420, 385},

{-3839, 4354, -1460, -1460, 4354, -3839},

{46081, -56490, 26684, -11760, 26684, -56490, 46081},

{-645119, 836296, -418936, 92624, 92624, -418936, 836296, -645119},

{10321921, -14026824, 7562120, -2189376, 718368, -2189376, 7562120, -14026824, 10321921},

{-185794559, 262803366, -150102120, 46239920, -7606032, -7606032, 46239920, -150102120, 262803366, -185794559},

{3715891201, -5441863790, 3264920736, -1076561200, 221207888, -57731520, 221207888, -1076561200, 3264920736, -5441863790, 3715891201}

Clear[p, x, n, b, a, b0];

p[x_, n_] := Product[x - (2*i), {i, 0, Floor[n/2]}]/x;

Table[Expand[ CoefficientList[ExpandAll[p[x, n]], x] + Reverse[CoefficientList[ExpandAll[p[x, n]], x]]], {n, 0, 20, 2}];

Flatten[%]

A039683, A039757

Sequence in context: A108558 A128434 A119731 this_sequence A054768 A104251 A153731

Adjacent sequences: A155715 A155716 A155717 this_sequence A155719 A155720 A155721

uned,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 25 2009