A105619 - OEIS

%I #5 Jun 13 2017 01:36:27

%S 1,-2,1,-2,-4,1,-10,-2,-6,1,-74,-10,-2,-8,1,-706,-74,-10,-2,-10,1,

%T -8162,-706,-74,-10,-2,-12,1,-110410,-8162,-706,-74,-10,-2,-14,1,

%U -1708394,-110410,-8162,-706,-74,-10,-2,-16,1,-29752066,-1708394,-110410,-8162,-706,-74,-10,-2,-18,1

%N Matrix inverse of triangle A105615.

%C Except for the initial few terms, all columns are equal to negative A000698 (related to double factorials).

%e Triangle begins:

%e 1;

%e -2,1;

%e -2,-4,1;

%e -10,-2,-6,1;

%e -74,-10,-2,-8,1;

%e -706,-74,-10,-2,-10,1;

%e -8162,-706,-74,-10,-2,-12,1;

%e -110410,-8162,-706,-74,-10,-2,-14,1;

%e -1708394,-110410,-8162,-706,-74,-10,-2,-16,1; ...

%o (PARI) T(n,k)=if(n<k || k<0,0, matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))[n+1,k+1])

%Y Cf. A105615, A000698, A105620 (matrix square-root).

%K sign,tabl

%O 0,2

%A _Paul D. Hanna_, Apr 16 2005