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 A024000 #35 May 15 2025 12:04:37
%S A024000 1,0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,
%T A024000 -19,-20,-21,-22,-23,-24,-25,-26,-27,-28,-29,-30,-31,-32,-33,-34,-35,
%U A024000 -36,-37,-38,-39,-40,-41,-42,-43,-44,-45,-46,-47,-48,-49,-50,-51,-52,-53,-54,-55,-56
%N A024000 a(n) = 1 - n.
%C A024000 a(n) is the weighted sum over all derangements (permutations with no fixed points) of n elements where each permutation with an odd number of cycles has weight +1 and each with an even number of cycles has weight -1. [_Michael Somos_, Jan 19 2011]
%H A024000 Vincenzo Librandi, <a href="/A024000/b024000.txt">Table of n, a(n) for n = 0..1000</a>
%H A024000 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A024000 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A024000 E.g.f.: (1-x)*exp(x).
%F A024000 a(n) = Sum_{k=0..n} A094816(n,k)*(-1)^k (alternating row sums of Poisson-Charlier coefficient matrix).
%F A024000 O.g.f.: (1-2*x)/(1-x)^2. a(n+1) = A001489(n). - _R. J. Mathar_, May 28 2008
%F A024000 a(n) = 2*a(n-1)-a(n-2) for n>1. - _Wesley Ivan Hurt_, Mar 02 2016
%e A024000 a(4) = -3 because there are 6 derangements with one 4-cycle with weight -1 and 3 derangements with two 2-cycles with weight +1. - _Michael Somos_, Jan 19 2011
%p A024000 A024000:=n->1-n: seq(A024000(n), n=0..100); # _Wesley Ivan Hurt_, Mar 02 2016
%t A024000 CoefficientList[Series[(1 - 2 x)/(1 - x)^2, {x, 0, 60}], x] Range[0, 60]!
%t A024000 CoefficientList[Series[Exp[x] (1 - x), {x, 0, 60}], x]
%t A024000 1-Range[0,60] (* _Harvey P. Dale_, Sep 18 2013 *)
%t A024000 Flatten[NestList[(#/.x_/;x>1->Sequence[x,2x])-1&,{1},60]]
%t A024000 (* _Robert G. Wilson v_, Mar 02 2016 *)
%o A024000 (PARI) {a(n) = 1 - n} /* _Michael Somos_, Jan 19 2011 */
%o A024000 (Magma) [1-n: n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011
%Y A024000 Cf. A000007, A000166, A087981, A137775. - _Michael Somos_, Jan 19 2011
%Y A024000 Cf. A001489, A094816.
%Y A024000 A022958 shifted left.
%K A024000 sign,easy
%O A024000 0,4
%A A024000 _N. J. A. Sloane_