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

%I

%S 1,1,10,1,13,113,1,16,171,1526,1,19,241,2551,24337,1,22,323,3956,

%T 43653,450066,1,25,417,5801,72689,850809,9492289,1,28,523,8146,114265,

%U 1496944,18689527,225159022,1,31,641,11051,171561,2487171,34358881,557947691

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

%C Denominator A099615.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BernoulliInequality.html">Bernoulli Inequality</a>

%e Triangle (1+1/n)^k - (1+k/n) starts, 2<=k<=n<=6:

%e n=2: .................. 1/4,

%e n=3: .............. 1/9 ____ 10/27,

%e n=4: ......... 1/16 ___ 13/64 ___ 113/256,

%e n=5: ..... 1/25 __ 16/125 __ 171/625 __ 1526/3125,

%e n=6: . 1/36 _ 19/216 _ 241/1296 _ 2551/7776 _ 24337/46656.

%Y Cf. A099614.

%K nonn,tabl,frac

%O 1,3

%A _Reinhard Zumkeller_, Oct 25 2004

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)