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 A158050 #10 Nov 27 2015 00:30:50 %S A158050 5040,-4137840,99515142720,-1122871063189680,9688118420572305840, %T A158050 -150299359081533202947840,1405831144255746621131643120, %U A158050 -18442639987146150894175704882480,203561673763315319923663885655833920 %N A158050 Determinant of power series with alternate signs of gamma matrix with determinant 7!. %C A158050 a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n) %C A158050 where A is the submatrix A(1..8,1..8) of the matrix with factorial determinant %C A158050 A= [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!. %C A158050 a(n) is even with respect to signs of power of A. %D A158050 G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008 %e A158050 a(1) = Determinant(A) = 7! = 5040. %p A158050 seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..20); %Y A158050 Cf. A111490, A158040-A158049. %K A158050 sign %O A158050 0,1 %A A158050 _Giorgio Balzarotti_ & _Paolo P. Lava_, Mar 11 2009