OFFSET
0,13
COMMENTS
Symmetric q-binomial coefficients are based on symmetric q-numbers [n] := (q^n-1/q^n)/(q-1/q).
FORMULA
EXAMPLE
Triangle begins:
n\k| 0 1 2 3 4 5 6 7 ...
---+----------------
0 | 1
1 | 1 1
2 | 1 0 1
3 | 1 1 1 1
4 | 1 0 2 0 1
5 | 1 1 2 2 1 1
6 | 1 0 3 0 3 0 1
7 | 1 1 3 5 5 3 1 1
...
MATHEMATICA
T[ n_, k_] := Coefficient[ QBinomial[ n, k, x^2] / x^(k (n - k)) // FunctionExpand // Expand, x, 0];
PROG
(PARI) {T(n, k) = if( k<0 || k>n, 0, polcoeff( prod(j = 1, k, (x^(n+1-j) - x^(-n-1+j))/(x^j - x^(-j))), 0))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 19 2020
STATUS
approved