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Lower triangular matrix T = Pascal lower triangular matrix divided on the left by its entry-square.
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%I #8 Oct 30 2015 10:18:19

%S 1,0,1,0,-2,1,0,12,-6,1,0,-132,66,-12,1,0,2280,-1140,210,-20,1,0,

%T -56760,28380,-5240,510,-30,1,0,1923600,-961800,177660,-17360,1050,

%U -42,1,0,-85149960,42574980,-7864920,769090,-46760,1932,-56,1

%N Lower triangular matrix T = Pascal lower triangular matrix divided on the left by its entry-square.

%C Reference is a solution to a problem of I. Gessel.

%D "Inverse of a Combinatorial Matrix", Dave Callan, American Mathematical Monthly, Vol. 95 (1988), pp. 770-771.

%F T=Inverse matrix of {a_ij}:{binomial(i, j)*binomial(j, j-i)}=[ A008459 ]^(-1)*[ A007318 ]

%e 1;

%e 0,1;

%e 0,-2,1;

%e 0,12,-6,1;

%e 0,-132,66,-12,1;

%e etc.

%Y A007318, A008459.

%K sign,tabl

%O 0,5

%A _Len Smiley_