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A232821 a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1).

%I A232821 #30 May 08 2025 23:00:05
%S A232821 1,1,6,52,549,7075,109172,1971026,40823443,954730001,24892154602,
%T A232821 716025676088,22528094057193,769646697066375,28375143175948712,
%U A232821 1122910795732014438,47478259662185188967,2136067435649547983973,101891594614083396452878
%N A232821 a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1).
%H A232821 Derek Orr, <a href="/A232821/b232821.txt">Table of n, a(n) for n = 1..100</a>
%F A232821 a(n) = n^(n-1) - A060946(n-1).
%F A232821 a(n) = A000169(n) - Sum_{k=1..n-1} A000169(k).
%e A232821 6^5 - 5^4 - 4^3 - 3^2 - 2^1 - 1^0 = 7075 so a(6) = 7075.
%t A232821 a[n_] := n^(n - 1) - Sum[i^(i - 1), {i, 1, n - 1}]; Table[a[n], {n, 20}] (* _Carlos Eduardo Olivieri_, May 29 2015 *)
%o A232821 (Python)
%o A232821 def sub(n):
%o A232821   num = n**(n-1)
%o A232821   for i in range(0, n-1):
%o A232821       num -= (i+1)**i
%o A232821   return num
%o A232821 n = 1
%o A232821 while n < 100:
%o A232821   print(sub(n), end=', ')
%o A232821   n += 1
%o A232821 (PARI) vector(20,n,n^(n-1)-sum(i=1,n-1,i^(i-1))) \\ _Derek Orr_, Apr 05 2015
%Y A232821 Cf. A060946, A000169.
%K A232821 nonn,easy
%O A232821 1,3
%A A232821 _Derek Orr_, Nov 30 2013
%E A232821 Name edited by _Derek Orr_, Apr 05 2015