|
%I #22 Feb 26 2018 09:14:32
%S 1,12,1080,224000,14817600000,186313420339200000,
%T 1033954523962885324800000,365356847125734485878112256000000,
%U 514390892189284848943526481454694400000000,15402297982638230438765209613012092908994560000000000,5520417482843902292560357271173454517680021278744903680000000000
%N a(n) is the denominator of det(I+H) where H is the n X n Hilbert matrix.
%H Robert Israel, <a href="/A295427/b295427.txt">Table of n, a(n) for n = 1..41</a>
%H MathOverflow, <a href="https://mathoverflow.net/questions/292585/determinant-of-identity-matrix-plus-hilbert-matrix/292602">Determinant of identity matrix plus Hilbert matrix</a>, 2018.
%F det(I+H) = Sum_{subsets S of {1,2,...,n}} Product_{1<=i<j<=|S|} (S_i-S_j)^2 / Product_{1<= i,j <= |S|} (S_i+S_j-1).
%p f := n -> denom(LinearAlgebra:-Determinant(LinearAlgebra:-IdentityMatrix(n)+LinearAlgebra:-HilbertMatrix(n))):
%p map(f, [$1..30]);
%t a[n_] := Det[IdentityMatrix[n] + HilbertMatrix[n]] // Denominator;
%t Array[a, 11] (* _Jean-François Alcover_, Feb 26 2018 *)
%o (PARI) A295427(n) = denominator( matdet( matrix(n,n,i,j,1/(i+j-1)+(i==j)) ) ); \\ _Max Alekseyev_, Feb 16 2018
%Y Numerators are given in A295426.
%K nonn,frac
%O 1,2
%A _Robert Israel_, Feb 12 2018
| 