%I M4313 N1806 #28 Oct 14 2023 23:49:55
%S 1,6,720,1512000,53343360000,31052236723200000,
%T 295415578275110092800000,45669605890716810734764032000000,
%U 114309087153174410876339218101043200000000,4620689394791469131629562883903627872698368000000000
%N An ill-conditioned determinant.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Ruperto Corso, <a href="/A002204/b002204.txt">Table of n, a(n) for n = 1..41</a>
%H M. Lotkin, <a href="https://doi.org/10.1090/S0025-5718-1955-0074919-9">A set of test matrices</a>, Math. Comp., 9 (1955), 153-161.
%F Recurrence: a(n) = binomial(2n-2,n-2)*binomial(2n-2,n-1)*(2n-1)*a(n-1) with a(1)=1.
%F a(n) ~ A^3 * 2^(n*(2*n-1) - 1/12) / (exp(1/4) * Pi^n * n^(3/4)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Feb 24 2019
%t Table[BarnesG[2*n + 1]/(n*BarnesG[n + 1]^4), {n, 1, 10}] (* _Vaclav Kotesovec_, Feb 24 2019 *)
%o (PARI) for(n=1,100,print1((-1)^(n+1)/matdet(matrix(n,n,i,j,if(i>1,1/(i+j-1),1)))", ")) /* _Ruperto Corso_, Dec 14 2011 */
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Herman P. Robinson_
%E More terms from _Ruperto Corso_, Dec 14 2011