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%I #2 Mar 30 2012 18:59:15
%S 1,-6,1,0,-120,1,0,0,-504,1,0,0,0,-1320,1,0,0,0,0,-2730,1,0,0,0,0,0,
%T -4896,1,0,0,0,0,0,0,-7980,1,0,0,0,0,0,0,0,-12144,1,0,0,0,0,0,0,0,0,
%U -17550,1,0,0,0,0,0,0,0,0,0,-24360,1
%N Bi-diagonal inverse of (3n)!/(3k)!.
%C Row sums are 1-A054776(n). Inverse of A119831.
%F Column k has g.f. x^k(1-b(k+1)x) where b(n)=3n(3n-2)(3n-1)=A054776(n).
%e Triangle begins
%e 1,
%e -6, 1,
%e 0, -120, 1,
%e 0, 0, -504, 1,
%e 0, 0, 0, -1320, 1,
%e 0, 0, 0, 0, -2730, 1,
%e 0, 0, 0, 0, 0, -4896, 1,
%e 0, 0, 0, 0, 0, 0, -7980, 1,
%e 0, 0, 0, 0, 0, 0, 0, -12144, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, -17550, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -24360, 1
%K easy,sign,tabl
%O 0,2
%A _Paul Barry_, May 25 2006
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