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A156916 General q-Narayana triangle sequence: 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}] 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..42.

FORMULA

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}]

EXAMPLE

{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}

MATHEMATICA

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}]

CROSSREFS

A001263

Sequence in context: A154337 A033933 A108267 * A173584 A166973 A157156

Adjacent sequences:  A156913 A156914 A156915 * A156917 A156918 A156919

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 18 2009

STATUS

approved

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Last modified February 19 10:40 EST 2018. Contains 299330 sequences. (Running on oeis4.)