Some axi-symmetric determinants with integers for elements. (Q1454357)

Verf. betrachtet \(n\)-reihige Determinanten der Form \[ \varDelta^p(\alpha,n)= \begin{vmatrix} \alpha & 1 & 1 & 1 & \ldots \\ 1 & \binom{2p}{\hfill p}& \binom{2p+1}{\hfill p+1}& \binom{2p+2}{\hfill p+2}&\ldots\\ 1& \binom{2p+1}{p}& \binom{2p+2}{\hfill p+1}&\binom{2p+3}{\hfill p+2}&\ldots\\ 1& \binom{2p+2}{p}& \binom{2p+3}{\hfill p+1}& \binom{2p+4}{\hfill p+2}&\ldots\\ .&.&.&.&\ldots \end{vmatrix}, \] \[ \qquad s_n^p=\begin{vmatrix} \binom{2p}{\hfill p}& \binom{2p+1}{\hfill p+1}&\binom{2p+2}{\hfill p+2}&\ldots\\ \binom{2p+1}{p}&\binom{2p+2}{\hfill p+1}&\binom{2p+3}{\hfill p+2}&\ldots\\ \binom{2p+2}{p}&\binom{2p+3}{\hfill p+1}&\binom{2p+4}{\hfill p+2}&\ldots\\ .&.&.&\ldots \end{vmatrix} \] und die Summe \(\sigma(\varDelta)\) bzw. \(\sigma(s)\) der ``signed primary minors''.