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

1,1

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

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! ].

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}]

Crossrefs

Cf. A045373.

Sequence in context: A054226 A000024 A005223 * A278457 A094116 A079476

Adjacent sequences: A118677 A118678 A118679 * A118681 A118682 A118683

Keyword

frac,nonn

Author

Alexander Adamchuk, May 19 2006, Dec 13 2006

Status

approved