A099613 Numerator of (1+1/n)^k - (1+k/n), 2<=k<=n, triangle read by rows.

1, 1, 10, 1, 13, 113, 1, 16, 171, 1526, 1, 19, 241, 2551, 24337, 1, 22, 323, 3956, 43653, 450066, 1, 25, 417, 5801, 72689, 850809, 9492289, 1, 28, 523, 8146, 114265, 1496944, 18689527, 225159022, 1, 31, 641, 11051, 171561, 2487171, 34358881, 557947691

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 ____ 10/27,
n=4: ......... 1/16 ___ 13/64 ___ 113/256,
n=5: ..... 1/25 __ 16/125 __ 171/625 __ 1526/3125,
n=6: . 1/36 _ 19/216 _ 241/1296 _ 2551/7776 _ 24337/46656.

Crossrefs

Cf. A099614.

Sequence in context: A073731 A179937 A198487 * A209924 A209926 A016530

Adjacent sequences: A099610 A099611 A099612 * A099614 A099615 A099616

Keyword

nonn,tabl,frac

Author

Reinhard Zumkeller, Oct 25 2004

Status

approved