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A047991
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Triangle formed from expansion of (x-1)(x+2)(x-3)...(x+-n).
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4
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1, 1, -1, 1, 1, -2, 1, -2, -5, 6, 1, 2, -13, -14, 24, 1, -3, -23, 51, 94, -120, 1, 3, -41, -87, 400, 444, -720, 1, -4, -62, 200, 1009, -2356, -3828, 5040, 1, 4, -94, -296, 2609, 5716, -22676, -25584, 40320, 1, -5, -130, 550, 5273, -17765, -74120, 178500, 270576, -362880
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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REFERENCES
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Studied by M. Bhargava (bhargava(AT)math.Princeton.EDU) and H. S. Wilf.
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LINKS
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EXAMPLE
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Triangle begins
1;
1, -1;
1, 1, -2;
1, -2, -5, 6;
1, 2, -13, -14, 24;
1, -3, -23, 51, 94, -120;
1, 3, -41, -87, 400, 444, -720;
1, -4, -62, 200, 1009, -2356, -3828, 5040;
1, 4, -94, -296, 2609, 5716, -22676, -25584, 40320;
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MATHEMATICA
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With[{nn=10}, Flatten[Table[Reverse[CoefficientList[Series[Times@@ Table[x+n (-1)^n, {n, i}], {x, 0, nn}], x]], {i, 0, nn}]]] (* Harvey P. Dale, Aug 28 2012 *)
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CROSSREFS
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A047990 gives sums of absolute values of rows.
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KEYWORD
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AUTHOR
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STATUS
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approved
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