0,5

Row sums are:

{1, 2, 0, 6, 4, 2, -152, -674, -20468, 1233722, 556704368,...}.

On the sequence only q=2 and q=3 are Integers,

the rest have a few rational terms.

q=2;m=1;

t(n,k)=If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {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, 2, 2, 1},

{1, 2, -2, 2, 1},

{1, -6, 6, 6, -6, 1},

{1, -14, -42, -42, -42, -14, 1},

{1, 26, 182, -546, -546, 182, 26, 1},

{1, 178, -2314, 16198, -48594, 16198, -2314, 178, 1},

{1, 90, -8010, -104130, 728910, 728910, -104130, -8010, 90, 1},

{1, -2382, 107190, 9539910, 124018830, 289377270, 124018830, 9539910, 107190, -2382, 1}

t[n_, m_] = If[m == 0, n!, Product[Sum[(-1)^i* StirlingS2[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

b[n_, k_, m_] = f[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}]

Sequence in context: A143187 A143209 A163994 this_sequence A054526 A113453 A003983

Adjacent sequences: A156590 A156591 A156592 this_sequence A156594 A156595 A156596

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 10 2009