This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101334 #31 Nov 12 2024 02:42:13
%S A101334 0,0,1,11,131,1829,29849,561399,11994247,287420489,7642052309,
%T A101334 223394306387,7123940054219,246181194216957,9165811757198641,
%U A101334 365836296342931439,15584321022199735823,705800730789742512401,33866021217511735389485,1716275655660313589123979
%N A101334 a(n) = n^n - (n+1)^(n-1).
%C A101334 b(n) = n^n mod (n+1)^(n-1) begins: 0, 0, 1, 11, 6, 533, 13042, 37111, 2428309, ... - _Alex Ratushnyak_, Aug 06 2012
%C A101334 a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 2. - _Geoffrey Critzer_, Jan 11 2013
%C A101334 Number of defective parking functions of length n and at least one defect. - _Alois P. Heinz_, Aug 18 2017
%H A101334 Alois P. Heinz, <a href="/A101334/b101334.txt">Table of n, a(n) for n = 0..386</a>
%H A101334 Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, and Pascal Schweitzer, <a href="https://arxiv.org/abs/0803.0302">Counting Defective Parking Functions</a>, arXiv:0803.0302 [math.CO], 2008.
%H A101334 Luca Ferrari and Francesco Verciani, <a href="https://arxiv.org/abs/2411.06876">On the enumeration of permutation-invariant and complete Naples parking functions</a>, arXiv:2411.06876 [math.CO], 2024. See p. 11.
%F A101334 E.g.f.: 1/(1-T(x)) - exp(T(x)) where T(x) is the e.g.f. for A000169. - _Geoffrey Critzer_, Jan 11 2013
%F A101334 a(n) = Sum_{k>0} A264902(n,k). - _Alois P. Heinz_, Nov 29 2015
%F A101334 a(n) = A000312(n) - A000272(n+1). - _Alois P. Heinz_, Aug 18 2017
%e A101334 a(3) = 3^3 - 4^2 = 27-16 = 11.
%t A101334 ReplacePart[Table[n^n-(n+1)^(n-1),{n,0,nn}],0,1] (* _Geoffrey Critzer_, Jan 11 2013 *)
%o A101334 (PARI) for(x=1,20,print( x^x-(x+1)^(x-1) ))
%o A101334 (Python)
%o A101334 print([n**n - (n+1)**(n-1) for n in range(33)]) # _Alex Ratushnyak_, Aug 06 2012
%Y A101334 Cf. A000272, A000312, A046065, A264902.
%K A101334 nonn
%O A101334 0,4
%A A101334 _Jorge Coveiro_, Dec 24 2004
%E A101334 a(0) prepended by _Alex Ratushnyak_, Aug 06 2012