A295427 a(n) is the denominator of det(I+H) where H is the n X n Hilbert matrix.

1, 12, 1080, 224000, 14817600000, 186313420339200000, 1033954523962885324800000, 365356847125734485878112256000000, 514390892189284848943526481454694400000000, 15402297982638230438765209613012092908994560000000000, 5520417482843902292560357271173454517680021278744903680000000000

Offset

1,2

Links

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

MathOverflow, Determinant of identity matrix plus Hilbert matrix, 2018.

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

Mathematica

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

Prog

(PARI) A295427(n) = denominator( matdet( matrix(n, n, i, j, 1/(i+j-1)+(i==j)) ) ); \\ Max Alekseyev, Feb 16 2018

Crossrefs

Numerators are given in A295426.

Sequence in context: A004812 A088671 A274117 * A354822 A260030 A160010

Adjacent sequences: A295424 A295425 A295426 * A295428 A295429 A295430

Keyword

nonn,frac

Author

Robert Israel, Feb 12 2018

Status

approved