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a(n) = floor(n^2*((n-1)/n)^(n-1/2)).
0

%I #9 Sep 02 2021 13:36:22

%S 0,1,3,5,9,13,17,23,29,36,44,52,62,72,82,94,106,119,132,147,162,178,

%T 194,211,229,248,268,288,309,331,353,376,400,425,450,476,503,531,559,

%U 588,618,648,680,712,744,778,812,847,883,919,956,994,1033,1072,1112,1153

%N a(n) = floor(n^2*((n-1)/n)^(n-1/2)).

%C From a mistake made in Stirling's approximation to a ratio of factorials that gives a relatively slow quadratic sequence.

%C Actually Stirling's ratio limit is: limit_{n-> Infinity} ((n-1)/n)^(n-1/2) = 1/e.

%t a=Table[Floor[n^2*((n-1)/n)^(n-1/2)], {n, 1, 200}]

%K nonn

%O 1,3

%A _Roger L. Bagula_, Aug 09 2004

%E Offset corrected by _Georg Fischer_, Aug 31 2021