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a(n) = n^n - n^2 with 0^0=1.
3

%I #8 Feb 09 2017 02:30:53

%S 1,0,0,18,240,3100,46620,823494,16777152,387420408,9999999900,

%T 285311670490,8916100448112,302875106592084,11112006825557820,

%U 437893890380859150,18446744073709551360

%N a(n) = n^n - n^2 with 0^0=1.

%F a(n) = A000312(n) - A000290(n) = log(A058125(n))/log(n).

%F E.g.f.: 1/(1 + LambertW(-x)) - x*(x + 1)*exp(x), where LambertW() is the Lambert W-function. - _Ilya Gutkovskiy_, Feb 08 2017

%e a(2) = 2^2 - 2^2 = 4 - 4 = 0.

%e a(3) = 3^3 - 3^2 = 27 - 9 = 18.

%Y Cf. A000290, A000312, A058125.

%K easy,nonn

%O 0,4

%A _Henry Bottomley_, Nov 10 2000