0,5

Row sums are:

{1, 2, 9, 72, 1087, 30134, 1599821, 161247076, 31779489531, 12145190181522,

9199299348551721,...}.

I have made the general Narayana level i equal to the m =q-1 q-combination / Gaussian level, but that is not necessary.

q=2;m=1;

c(n,l,m)=Product[q-binomial(n + k, l + k, m)/q-binomial(n - l + k, k, m), {k, 0, m}]

{1},

{1, 1},

{1, 7, 1},

{1, 35, 35, 1},

{1, 155, 775, 155, 1},

{1, 651, 14415, 14415, 651, 1},

{1, 2667, 248031, 1098423, 248031, 2667, 1},

{1, 10795, 4112895, 76499847, 76499847, 4112895, 10795, 1},

{1, 43435, 66982975, 5104102695, 21437231319, 5104102695, 66982975, 43435, 1},

{1, 174251, 1081227455, 333481439335, 5738032249719, 5738032249719, 333481439335, 1081227455, 174251, 1},

{1, 698027, 17375986111, 21563598763751, 1501800313901239, 6152536769853463, 1501800313901239, 21563598763751, 17375986111, 698027, 1}

Clear[t, n, m, i, k, c, b];

t[n_, m_] = If[m == 0, n!, Product[Sum[(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])]

c[n_, l_, m_] = Product[b[n + k, l + k, m]/b[n - l + k, k, m], {k, 0, m}]

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

A001263

Sequence in context: A154337 A033933 A108267 this_sequence A166973 A157156 A022170

Adjacent sequences: A156913 A156914 A156915 this_sequence A156917 A156918 A156919

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 18 2009