login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I

%S 1,1,1,1,31,1,1,806,806,1,1,20306,527956,20306,1,1,508431,333038706,

%T 333038706,508431,1,1,12714681,208533483081,5253698396331,

%U 208533483081,12714681,1,1,317886556,130381488829956,82245646088465706

%N 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 ))

%C q=2 is A156916.

%C Row sums are:

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

%C 34760211807180756108894, 25197394536008396774892947100,...}

%F q=5:

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

%F 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 ))

%e {1},

%e {1, 1},

%e {1, 31, 1},

%e {1, 806, 806, 1},

%e {1, 20306, 527956, 20306, 1},

%e {1, 508431, 333038706, 333038706, 508431, 1},

%e {1, 12714681, 208533483081, 5253698396331, 208533483081, 12714681, 1},

%e {1, 317886556, 130381488829956, 82245646088465706, 82245646088465706, 130381488829956, 317886556, 1},

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

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

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

%t 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 ));

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

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

%Y A156916

%K nonn,tabl,uned

%O 1,5

%A _Roger L. Bagula_, Jan 31 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)