A118680 Numerator of determinant of n X n matrix with M(i,j) = (i+1)/i if i=j otherwise 1.

2, 2, 7, 11, 2, 11, 29, 37, 23, 1, 67, 79, 23, 53, 11, 137, 1, 43, 191, 211, 29, 127, 277, 43, 163, 1, 379, 37, 109, 233, 71, 23, 281, 149, 631, 1, 1, 53, 71, 821, 431, 113, 947, 991, 1, 541, 1129, 107, 613, 1

Offset: 1

Author

Alexander Adamchuk, May 19 2006, Dec 13 2006

Keywords

• frac
• nonn

Comments

Some a(n) are equal to 1 (n=10,17,26,36,37,45..). It appears that all other a(n) are primes congruent to {0, 1, 2, 4} mod 7 - A045373.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045373.

Programs

Mathematica

Numerator[Table[ Det[ DiagonalMatrix[ Table[ 1/i, {i, 1, n} ] ] + 1 ], {n, 1, 80} ]]
Table[Numerator[(1+n(n+1)/2)/n! ],{n,1,100}]

Formula

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

a(n) = Numerator[ (1 + Sum[ k, {k,1,n} ]) /Product[ k, {k,1,n} ] ]. a(n) = Numerator[ (1 + n(n+1)/2) / n! ].