A075845 Associated to determinants of skew-symmetric matrices related to Catalan-numbers or central binomial coefficients.

1, 2, 6, 31, 286, 4600, 130664, 6619840, 591478944, 93683332808, 26438906945728, 13204957909414302, 11705869922500953011, 18478647155522687153022, 51703789444327985876248510, 256918480515843999119385185643, 2272506643204540750098828441592950

Offset: 1

Author

Roland Bacher, Oct 15 2002

Keywords

• nonn

Comments

Appears to be the Hankel transform of A127632. - Paul Barry, Jan 20 2007

Links

• Roland Bacher, Determinants of matrices related to the Pascal triangle, Journal de Théorie des Nombres de Bordeaux 14 (2002), 19-41.

Crossrefs

Cf. A000108.

Formula

a(n) = sqrt(det(M(2*n))) where M(2*n) is the 2n X 2n matrix with entries defined by m(i,0)=alpha(i), m(0,j)=beta(j), m(i,j) = m(i-1,j)+m(i,j-1) (using indexing 0..2n-1 for rows and columns), alpha = 0, 1, 1, 2, 5, 14, 42, ... = Catalan numbers (A000108) shifted by 1 position and beta(k) = -alpha(k) [from Bacher]. - Sean A. Irvine, Mar 10 2025

Extensions

a(17) from Sean A. Irvine, Mar 10 2025