A295426 a(n) is the numerator of det(I+H) where H is the n X n Hilbert matrix.

2, 29, 2927, 659251, 46508430817, 616473989937916861, 3577562384224548869428843, 1314142513507030576449489451528961, 1914627150738259149750867704875720944260093, 59112836238579742851313392516538890376380560892536927, 21782568597204534349136837897139663659824535306651051308429796609

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..41

MathOverflow, Determinant of identity matrix plus Hilbert matrix

Formula

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).

Maple

f := n -> numer(LinearAlgebra:-Determinant(LinearAlgebra:-IdentityMatrix(n)+LinearAlgebra:-HilbertMatrix(n))):
map(f, [$1..30]);

Mathematica

a[n_] := Det[IdentityMatrix[n] + HilbertMatrix[n]] // Numerator;
Array[a, 11] (* Jean-François Alcover, Feb 26 2018 *)

Prog

(PARI) A295426(n) = numerator( matdet( matrix(n, n, i, j, 1/(i+j-1)+(i==j)) ) ); \\ Max Alekseyev, Feb 16 2018

Crossrefs

Denominators in A295427.

Sequence in context: A059725 A112784 A252042 * A055559 A350858 A345041

Adjacent sequences: A295423 A295424 A295425 * A295427 A295428 A295429

Keyword

nonn,frac

Author

Robert Israel, Feb 12 2018

Status

approved