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

%I A099613 #4 Feb 16 2025 08:32:55
%S A099613 1,1,10,1,13,113,1,16,171,1526,1,19,241,2551,24337,1,22,323,3956,
%T A099613 43653,450066,1,25,417,5801,72689,850809,9492289,1,28,523,8146,114265,
%U A099613 1496944,18689527,225159022,1,31,641,11051,171561,2487171,34358881,557947691
%N A099613 Numerator of (1+1/n)^k - (1+k/n), 2<=k<=n, triangle read by rows.
%C A099613 Denominator A099615.
%H A099613 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BernoulliInequality.html">Bernoulli Inequality</a>
%e A099613 Triangle (1+1/n)^k - (1+k/n) starts, 2<=k<=n<=6:
%e A099613 n=2: .................. 1/4,
%e A099613 n=3: .............. 1/9 ____ 10/27,
%e A099613 n=4: ......... 1/16 ___ 13/64 ___ 113/256,
%e A099613 n=5: ..... 1/25 __ 16/125 __ 171/625 __ 1526/3125,
%e A099613 n=6: . 1/36 _ 19/216 _ 241/1296 _ 2551/7776 _ 24337/46656.
%Y A099613 Cf. A099614.
%K A099613 nonn,tabl,frac
%O A099613 1,3
%A A099613 _Reinhard Zumkeller_, Oct 25 2004