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A295427
a(n) is the denominator of det(I+H) where H is the n X n Hilbert matrix.
2
1, 12, 1080, 224000, 14817600000, 186313420339200000, 1033954523962885324800000, 365356847125734485878112256000000, 514390892189284848943526481454694400000000, 15402297982638230438765209613012092908994560000000000, 5520417482843902292560357271173454517680021278744903680000000000
OFFSET
1,2
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
KEYWORD
nonn,frac
AUTHOR
Robert Israel, Feb 12 2018
STATUS
approved