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A214698 a(n) = (n^n - n^2)/2.

%I A214698 #22 Jul 04 2025 17:52:14
%S A214698 0,0,9,120,1550,23310,411747,8388576,193710204,4999999950,
%T A214698 142655835245,4458050224056,151437553296042,5556003412778910,
%U A214698 218946945190429575,9223372036854775680,413620130943168381944,19673204037648268787550,989209827830156794561809,52428799999999999999999800
%N A214698 a(n) = (n^n - n^2)/2.
%H A214698 Harvey P. Dale, <a href="/A214698/b214698.txt">Table of n, a(n) for n = 1..386</a>
%F A214698 a(n) = A214647(n) - n^2 = A117694(n) - A000217(n).
%F A214698 E.g.f.: (-1/2)*(lambertW(-x)/(1 + lambertW(-x)) + x*(x+1)*exp(x)). - _G. C. Greubel_, Jan 08 2024
%e A214698 a(3) = (27 - 9)/2 = 9.
%p A214698 A214698:= proc(n)
%p A214698     (n^n-n^2)/2 ;
%p A214698 end proc: # _R. J. Mathar_, Aug 07 2012
%t A214698 Table[(n^n-n^2)/2,{n,30}] (* _Harvey P. Dale_, Dec 25 2022 *)
%o A214698 (Python)
%o A214698 for n in range(1, 22):
%o A214698     print((n**n - n*n)//2)
%o A214698 (Magma) [(n^n -n^2)/2: n in [1..30]]; // _G. C. Greubel_, Jan 08 2024
%o A214698 (SageMath) [(n^n -n^2)/2 for n in range(1,31)] # _G. C. Greubel_, Jan 08 2024
%Y A214698 Cf. A124797 is essentially equal to (n^n-n)/2.
%Y A214698 Cf. A000217, A117694, A214647.
%K A214698 nonn,easy
%O A214698 1,3
%A A214698 _Alex Ratushnyak_, Jul 26 2012