A118679 Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.

1, 2, 1, 13, 19, 13, 17, 43, 53, 1, 19, 89, 103, 59, 67, 151, 13, 47, 1, 229, 251, 137, 149, 1, 349, 47, 101, 433, 463, 1, 263, 43, 593, 157, 83, 701, 739, 389, 409, 859, 53, 59, 1, 1033, 83, 563, 587, 1223, 67, 331, 1, 1429, 1483, 769, 797, 127, 1709, 1, 457, 1889

Offset

1,2

Comments

Numbers n such that a(n) = 1 are listed in A127852.

All a(n)>1 are prime belonging to A038889 (i.e., 17 is a square mod a(n)).

Links

Table of n, a(n) for n=1..60.

Formula

det(M) = (-1)^(n+1)*(n^2+3*n-2)/(2*(n+1)!), implying that a(n)=p, where p=A006530(n^2+3*n-2) is the largest prime divisor of (n^2+3*n-2), if p>n+1 or p=sqrt((n^2+3*n-2)/2); otherwise a(n)=1.

a(n) = Numerator[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ]].

a(n) = Numerator[ (n^2+3n-2)/(2(n+1)!) ] = Numerator[ ((2n+3)^2-17)/(4(n+1)!) ].

Mathematica

Numerator[Table[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ], {n, 1, 70} ]]
Table[ Numerator[ (n^2+3n-2)/(2(n+1)!) ], {n, 1, 100} ]

Crossrefs

Cf. A038889.

Cf. A118680, A127852, A127853.

Sequence in context: A113097 A032001 A358205 * A087451 A063558 A174170

Adjacent sequences: A118676 A118677 A118678 * A118680 A118681 A118682

Keyword

frac,nonn

Author

Alexander Adamchuk, May 19 2006, Feb 03 2007

Extensions

Edited by Max Alekseyev, Jun 02 2009

Status

approved