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Search: id:A130595
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| A130595 |
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Triangle T(n,k), read by rows,given by [ -1,0,0,0,0,0,...] DELTA [[1,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . |
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+0
15
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| 1, -1, 1, 1, -2, 1, -1, 3, -3, 1, 1, -4, 6, -4, 1, -1, 5, -10, 10, -5, 1, 1, -6, 15, -20, 15, -6, 1, -1, 7, -21, 35, -35, 21, -7, 1, 1, -8, 28, -56, 70, -56, 28, -8, 1, -1, 9, -36, 84, -126, 126, -84, 36, -9, 1, 1, -10, 45, -120, 210, -252, 210, -120, 45, -10, 1, -1, 11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Inverse of A007318 (as an infinite lower triangular matrix). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 21 2007
Coefficients of the polynomials generated by the e.g.f. exp(x*t)*exp(-t). [From Peter Luschny (peter(AT)luschny.de), Jul 13 2009]
Riordan array (1/(1+x), x/(1+x)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 29 2009]
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FORMULA
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T(n,k)=(-1)^(n-k)*binomial(n,k)=(-1)^(n-k)*A007318(n,k) .
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EXAMPLE
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Triangle begins:
1;
-1, 1;
1, -2, 1;
-1, 3, -3, 1;
1, -4, 6, -4, 1;
-1, 5, -10, 10, -5, 1;
1, -6, 15, -20, 15, -6, 1;
-1, 7, -21, 35, -35, 21, -7, 1;
1, -8, 28, -56, 70, -56, 28, -8, 1;
-1, 9, -36, 84, -126, 126, -84, 36, -9, 1 ;...
Contribution from Peter Luschny (peter(AT)luschny.de), Jul 13 2009: (Start)
+ 1
- 1 + 1 x
+ 1 - 2 x + 1 x^2
- 1 + 3 x - 3 x^2 + 1 x^3
+ 1 - 4 x + 6 x^2 - 4 x^3 + 1 x^4 (End)
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MAPLE
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with(combstruct):for n from 0 to 11 do seq((-1)^(n-m)*count(Combination(n), size=m), m = 0 .. n) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 09 2008
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CROSSREFS
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Sequence in context: A118433 A007318 A108086 this_sequence A108363 A076831 A119724
Adjacent sequences: A130592 A130593 A130594 this_sequence A130596 A130597 A130598
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KEYWORD
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sign,tabl,new
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 17 2007
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