0,5

Row sums are:

{1, 2, 0, 34, 1346, 1012482, -3131215358, 121999780331522,

34591292869081661442, 107137531255480378706493442,

-3432787564907030237721525583871998,...}.

m=2;q=3:

t(n,m)=If[m == 0, n!, Product[Product[1 - (2*i - 1)*( m + 1), {i, 0, k - 1}], {k, 1, n}]];

b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

{1},

{1, 1},

{1, -2, 1},

{1, 16, 16, 1},

{1, -224, 1792, -224, 1},

{1, 4480, 501760, 501760, 4480, 1},

{1, -116480, 260915200, -3652812800, 260915200, -116480, 1},

{1, 3727360, 217081446400, 60782804992000, 60782804992000, 217081446400, 3727360, 1},

{1, -141639680, 263971038822400, -1921709162627072000, 38434183252541440000, -1921709162627072000, 263971038822400, -141639680, 1},

{1, 6232145920, 441359576911052800, 102819127037198860288000, 53465946059343407349760000, 53465946059343407349760000, 102819127037198860288000, 441359576911052800, 6232145920, 1},

{1, -311607296000, 970991069204316160000, -8595679020309824720076800000, 143032098897955483342077952000000, -3718834571346842566894026752000000, 143032098897955483342077952000000, -8595679020309824720076800000, 970991069204316160000, -311607296000, 1}

t[n_, m_] = If[m == 0, n!, Product[Product[1 - (2*i - 1)*( m + 1), {i, 0, k - 1}], {k, 1, n}]];

b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];

Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]

A156690, A156691, A156692, A156693

Sequence in context: A132318 A078089 A095836 this_sequence A154991 A090163 A124001

Adjacent sequences: A156694 A156695 A156696 this_sequence A156698 A156699 A156700

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 13 2009