OFFSET
0,3
COMMENTS
FORMULA
Conjecture: the n-th central term of the matrix inverse of the triangle of Gaussian binomial coefficients in q is divisible by [(q^(n+1)-1)/(q-1) * q^(n*(n-1)/2)] for n>=0 and integer q > 1.
MATHEMATICA
Table[(-1)^n QBinomial[2n, n, 2]/(2^(n+1) - 1), {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)
PROG
(PARI) a(n)=local(q=2, A=matrix(2*n+1, 2*n+1, n, k, if(n>=k, if(n==1 || k==1, 1, prod(j=n-k+1, n-1, 1-q^j)/prod(j=1, k-1, 1-q^j))))^-1); A[2*n+1, n+1]/( (q^(n+1)-1)/(q-1) * q^(n*(n-1)/2) )
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Dec 13 2007
STATUS
approved