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 A213203 #23 Mar 21 2013 16:50:08
%S A213203 -1,-1,3,132,4260,172440,9069480,609618240,51209444160,5267273961600,
%T A213203 651825357321600,95601055094899200,16405141092269529600,
%U A213203 3257166195621552614400,741005309513165913216000
%N A213203 The sum of the first n! integers, with every n-th integer taken as negative.
%H A213203 R. J. Cano, <a href="/A213203/b213203.txt">Table of n, a(n) for n = 1..60</a>
%H A213203 R. J. Cano, <a href="/wiki/First_sum_everything_then_subtract_twice">Additional information</a>
%F A213203 a(n) = n * (n-1)! * ((n-2)*(n-1)! - 1)/2.
%F A213203 Conjecture: a(n) + (-n^2-n-11)*a(n-1) + (n^3+7*n^2-13*n+39)*a(n-2) - 2*(n-2)*(4*n^2-2*n-15)*a(n-3) + 20*(n-2)*(n-3)*(n-4)*a(n-4) = 0. - _R. J. Mathar_, Mar 21 2013
%e A213203 For a(3)=3, 3! is 6 then the sum of the first 6 integers taking each 3rd integer as negative is: 1+2-3+4+5-6 = 3.
%e A213203 For a(4)=132, 4! is 24 then the sum of the first 24 integers taking each 4th integer as negative is: 1+2+3-4+5+6+7-8+9+10+11-12+13+14+15-16+17+18+19-20+21+22+23-24 = 132.
%o A213203 (PARI) a(n)={my(y=(n-1)!);((n*y)*((n-2)*y-1))\2;}
%Y A213203 Cf. A181482, A055555.
%K A213203 sign,easy
%O A213203 1,3
%A A213203 _R. J. Cano_, Mar 01 2013