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A118680
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Numerator of determinant of n X n matrix with M(i,j) = (i+1)/i if i=j otherwise 1.
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3
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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, 1327, 197, 179, 743, 67, 1597, 827, 107, 1, 1831, 1, 977, 2017
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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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! ].
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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}]
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CROSSREFS
| Cf. A045373.
Sequence in context: A054226 A000024 A005223 * A094116 A079476 A005298
Adjacent sequences: A118677 A118678 A118679 * A118681 A118682 A118683
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), May 19 2006, Dec 13 2006
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