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A173142 a(n) = n^n - (n-1)^(n-1) - (n-2)^(n-2) - ... - 1.

%I A173142 #12 Sep 08 2022 08:45:50
%S A173142 1,3,22,224,2837,43243,773474,15903604,369769661,9594928683,
%T A173142 274906599294,8620383706328,293663289402069,10799919901775579,
%U A173142 426469796631518922,17997426089579351788,808344199828497012733
%N A173142 a(n) = n^n - (n-1)^(n-1) - (n-2)^(n-2) - ... - 1.
%H A173142 G. C. Greubel, <a href="/A173142/b173142.txt">Table of n, a(n) for n = 1..250</a>
%F A173142 a(n) = 2*(n^n) - A001923(n), for n > 0. - _Kritsada Moomuang_, Feb 11 2019
%e A173142 1^1 - 0 = 1,
%e A173142 2^2 - 1 = 3,
%e A173142 3^3 - 2^2 - 1 = 22,
%e A173142 4^4 - 3^3 - 2^2 - 1 = 224, ...
%t A173142 f[n_]:=n^n; lst={};Do[a=f[n];Do[a-=f[m],{m,n-1,1,-1}];AppendTo[lst, a],{n,30}];lst
%t A173142 Table[n^n -Sum[(n-k)^(n-k), {k,1,n-1}], {n, 1, 20}] (* _G. C. Greubel_, Feb 11 2019 *)
%o A173142 (PARI) {a(n) = n^n - sum(k=1,n-1, (n-k)^(n-k))}; \\ _G. C. Greubel_, Feb 11 2019
%o A173142 (Magma) [n^n - (&+[(n-k)^(n-k): k in [1..n-1]]): n in [1..20]]; // _G. C. Greubel_, Feb 11 2019
%o A173142 (Sage) [n^n - sum((n-k)^(n-k) for k in (1..n-1)) for n in (1..20)] # _G. C. Greubel_, Feb 11 2019
%Y A173142 Cf. A001923.
%K A173142 nonn
%O A173142 1,2
%A A173142 _Vladimir Joseph Stephan Orlovsky_, Feb 10 2010