A295426 - OEIS

%I #23 Feb 26 2018 09:14:25

%S 2,29,2927,659251,46508430817,616473989937916861,

%T 3577562384224548869428843,1314142513507030576449489451528961,

%U 1914627150738259149750867704875720944260093,59112836238579742851313392516538890376380560892536927,21782568597204534349136837897139663659824535306651051308429796609

%N a(n) is the numerator of det(I+H) where H is the n X n Hilbert matrix.

%H Robert Israel, <a href="/A295426/b295426.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>

%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 -> numer(LinearAlgebra:-Determinant(LinearAlgebra:-IdentityMatrix(n)+LinearAlgebra:-HilbertMatrix(n))):

%p map(f, [$1..30]);

%t a[n_] := Det[IdentityMatrix[n] + HilbertMatrix[n]] // Numerator;

%t Array[a, 11] (* _Jean-François Alcover_, Feb 26 2018 *)

%o (PARI) A295426(n) = numerator( matdet( matrix(n,n,i,j,1/(i+j-1)+(i==j)) ) ); \\ _Max Alekseyev_, Feb 16 2018

%Y Denominators in A295427.

%K nonn,frac

%O 1,1

%A _Robert Israel_, Feb 12 2018