A128562 Triangle, read by rows, where T(n,k) is the coefficient of q^((n+1)*k) in the q-binomial coefficient [2*n+1, n] for n >= k >= 0.
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 6, 12, 6, 1, 1, 10, 29, 29, 10, 1, 1, 14, 61, 94, 61, 14, 1, 1, 21, 120, 263, 263, 120, 21, 1, 1, 29, 222, 645, 910, 645, 222, 29, 1, 1, 41, 392, 1468, 2724, 2724, 1468, 392, 41, 1, 1, 55, 669, 3113, 7352, 9686, 7352, 3113, 669, 55, 1
Offset: 0
Examples
Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins: 1; 1, 1; 1, 2, 1; 1, 4, 4, 1; 1, 6, 12, 6, 1; 1, 10, 29, 29, 10, 1; 1, 14, 61, 94, 61, 14, 1; 1, 21, 120, 263, 263, 120, 21, 1; 1, 29, 222, 645, 910, 645, 222, 29, 1; 1, 41, 392, 1468, 2724, 2724, 1468, 392, 41, 1; 1, 55, 669, 3113, 7352, 9686, 7352, 3113, 669, 55, 1; ...
Crossrefs
Programs
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PARI
T(n,k)=if(n
Formula
T(n,k) = [q^((n+1)*k)] Product_{j=n+1..2*n+1}(1-q^j) / Product_{j=1..n+1}(1-q^j).
Extensions
Minor edits by Petros Hadjicostas, Jun 01 2020
Comments