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A172302 q-form Narayana triangle sequence:q=5:c(n,q)=Product[(1 - q^i), {i, 1, n}]; w(n,m,q)=-(q - 1)*c(n - 1, q)*c(n, q)/(c(m - 1, q)* c(n - m, q)*c(m - 1, q)*c(n - m + 1, q)*(1 - q^m )) 0
1, 1, 1, 1, 31, 1, 1, 806, 806, 1, 1, 20306, 527956, 20306, 1, 1, 508431, 333038706, 333038706, 508431, 1, 1, 12714681, 208533483081, 5253698396331, 208533483081, 12714681, 1, 1, 317886556, 130381488829956, 82245646088465706 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

q=2 is A156916.

Row sums are:

{1, 2, 33, 1614, 568570, 667094276, 5670790791857, 164752055790364438,

34760211807180756108894, 25197394536008396774892947100,...}

LINKS

Table of n, a(n) for n=1..32.

FORMULA

q=5:

c(n,q)=Product[(1 - q^i), {i, 1, n}];

w(n,m,q)=-(q - 1)*c(n - 1, q)*c(n, q)/(c(m - 1, q)* c(n - m, q)*c(m - 1, q)*c(n - m + 1, q)*(1 - q^m ))

EXAMPLE

{1},

{1, 1},

{1, 31, 1},

{1, 806, 806, 1},

{1, 20306, 527956, 20306, 1},

{1, 508431, 333038706, 333038706, 508431, 1},

{1, 12714681, 208533483081, 5253698396331, 208533483081, 12714681, 1},

{1, 317886556, 130381488829956, 82245646088465706, 82245646088465706, 130381488829956, 317886556, 1},

{1, 7947261556, 81494438892517456, 1285577907930958734456, 32188893002425159081956, 1285577907930958734456, 81494438892517456, 7947261556, 1},

{1, 198682027181, 50934775370442204956, 20088685264446025720234456, 12578608531804976792602006956, 12578608531804976792602006956, 20088685264446025720234456, 50934775370442204956, 198682027181, 1}

MATHEMATICA

c[n_, q_] = Product[(1 - q^i), {i, 1, n}];

w[n_, m_, q_] = -(q - 1)*c[n - 1, q]*c[n, q]/(c[m - 1, q]*c[n - m, q]*c[m - 1, q]*c[n - m + 1, q]*(1 - q^m ));

Table[Table[Table[w[n, m, q], {m, 1, n}], {n, 1, 10}], {q, 2, 12}]

Table[Flatten[Table[Table[w[n, m, q], {m, 1, n}], {n, 1, 10}]], {q, 2, 12}]

CROSSREFS

A156916

Sequence in context: A300656 A239633 A174692 * A103474 A047687 A040953

Adjacent sequences:  A172299 A172300 A172301 * A172303 A172304 A172305

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 31 2010

STATUS

approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)