A099614 Numerator of (1-1/n)^k - (1-k/n), 2<=k<=n, triangle read by rows.

1, 1, 8, 1, 11, 81, 1, 14, 131, 1024, 1, 17, 193, 1829, 15625, 1, 20, 267, 2974, 29849, 279936, 1, 23, 353, 4519, 52113, 561399, 5764801, 1, 26, 451, 6524, 84997, 1034270, 11994247, 134217728, 1, 29, 561, 9049, 131441, 1782969, 23046721, 287420489

Offset

1,3

Comments

Denominator A099615.

Links

Table of n, a(n) for n=1..44.

Eric Weisstein's World of Mathematics, Bernoulli Inequality

Example

Triangle (1-1/n)^k - (1-k/n) starts, 2<=k<=n<=6:
n=2: .................. 1/4,
n=3: .............. 1/9 ____ 8/27,
n=4: ......... 1/16 ___ 11/64 ___ 81/256,
n=5: ..... 1/25 __ 14/125 __ 131/625 __ 1024/3125,
n=6: . 1/36 _ 17/216 _ 193/1296 _ 1829/7776 _ 15625/46656.

Crossrefs

Cf. A099613.

Sequence in context: A160925 A345059 A348973 * A032012 A092702 A070475

Adjacent sequences: A099611 A099612 A099613 * A099615 A099616 A099617

Keyword

nonn,tabl,frac

Author

Reinhard Zumkeller, Oct 25 2004

Status

approved