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A124645
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Triangle T(n,k), 0<=k<=n, read by rows given by [1,-1,0,0,0,0,0,...] DELTA [ -1,2,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
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1
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1, 1, -1, 0, 1, -1, 0, 1, -2, 1, 0, 0, 1, -2, 1, 0, 0, 1, -3, 3, -1, 0, 0, 0, 1, -3, 3, -1, 0, 0, 0, 1, -4, 6, -4, 1, 0, 0, 0, 0, 1, -4, 6, -4, 1, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Matrix inverse of A108299.
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FORMULA
| Row n has g.f.: x^[n/2]*(1-x)^(n-[n/2]).
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EXAMPLE
| Triangle begins:
1;
1, -1;
0, 1, -1;
0, 1, -2, 1;
0, 0, 1, -2, 1;
0, 0, 1, -3, 3, -1;
0, 0, 0, 1, -3, 3, -1;
0, 0, 0, 1, -4, 6, -4, 1;
0, 0, 0, 0, 1, -4, 6, -4, 1;
0, 0, 0, 0, 1, -5, 10, -10, 5, -1;
0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1;
0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1 ;...
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CROSSREFS
| Sequence in context: A164116 A164118 A180981 * A029409 A014674 A015339
Adjacent sequences: A124642 A124643 A124644 * A124646 A124647 A124648
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KEYWORD
| sign,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 13 2007, Aug 22 2007
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