A104560 - OEIS

%I #3 Mar 30 2012 18:36:45

%S 1,-1,1,1,-2,1,-2,5,-4,1,6,-16,15,-6,1,-30,81,-79,36,-9,1,204,-552,

%T 543,-256,72,-12,1,-1944,5262,-5184,2461,-712,132,-16,1,23340,-63180,

%U 62260,-29596,8615,-1640,220,-20,1,-360060,974670,-960520,456700,-133091,25475,-3500,350,-25,1,6692280,-18115800

%N Matrix inverse of triangle A104559, read by rows.

%C Column 0 is A104561.

%e Triangle begins:

%e 1;

%e -1,1;

%e 1,-2,1;

%e -2,5,-4,1;

%e 6,-16,15,-6,1;

%e -30,81,-79,36,-9,1;

%e 204,-552,543,-256,72,-12,1;

%e -1944,5262,-5184,2461,-712,132,-16,1;

%e 23340,-63180,62260,-29596,8615,-1640,220,-20,1;

%e -360060,974670,-960520,456700,-133091,25475,-3500,350,-25,1; ...

%o (PARI) {T(n,k)=local(M);M=matrix(n+1,n+1,m,j,if(m>=j, binomial(m-1-(j-1)\2,j\2)*binomial(m-1-j\2,(j-1)\2))); return((M^-1)[n+1,k+1])}

%Y Cf. A104559, A104561.

%K sign,tabl

%O 0,5

%A _Paul D. Hanna_, Mar 16 2005