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Matrix inverse of triangle A096651; transforms n-dimensional partitions into (n-1)-dimensional partitions.
2

%I #3 Mar 30 2012 18:36:41

%S 1,0,1,0,-1,1,0,0,-1,1,0,1,-1,-1,1,0,-1,3,-2,-1,1,0,-1,-1,5,-3,-1,1,0,

%T 3,-5,-1,7,-4,-1,1,0,4,-10,4,-2,9,-5,-1,1,0,-17,121,-146,42,-5,11,-6,

%U -1,1,0,-27,-662,1155,-591,130,-11,13,-7,-1,1,0,118,5952,-10015,5327,-1662,294,-21,15,-8,-1,1,0,267,-70266,113346,-57476

%N Matrix inverse of triangle A096651; transforms n-dimensional partitions into (n-1)-dimensional partitions.

%C Row sums form {1,1,0,0,0,...(zeros continue)}.

%e Rows begin:

%e [1],

%e [0,1],

%e [0,-1,1],

%e [0,0,-1,1],

%e [0,1,-1,-1,1],

%e [0,-1,3,-2,-1,1],

%e [0,-1,-1,5,-3,-1,1],

%e [0,3,-5,-1,7,-4,-1,1],

%e [0,4,-10,4,-2,9,-5,-1,1],

%e [0,-17,121,-146,42,-5,11,-6,-1,1],

%e [0,-27,-662,1155,-591,130,-11,13,-7,-1,1],

%e [0,118,5952,-10015,5327,-1662,294,-21,15,-8,-1,1],

%e [0,267,-70266,113346,-57476,17435,-3843,565,-36,17,-9,-1,1],

%e [0,-917,908722,-1473694,746476,-220017,46320,-7821,979,-57,19,-10,-1,1],...

%Y Cf. A096651.

%K sign,tabl

%O 0,18

%A _Paul D. Hanna_, Jul 13 2004