Search: id:A130595
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%I A130595
%S A130595 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,
%T A130595 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,
%U A130595 120,210,252,210,120,45,10,1,1,11,55,165,330,462,462,330,165,55,11,1
%V A130595 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,
%W A130595 -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,
%X A130595 210,-252,210,-120,45,-10,1,-1,11,-55,165,-330,462,-462,330,-165,55,-11,
               1
%N A130595 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 .
%C A130595 Inverse of A007318 (as an infinite lower triangular matrix). - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Aug 21 2007
%C A130595 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]
%C A130595 Riordan array (1/(1+x), x/(1+x)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 29 2009]
%F A130595 T(n,k)=(-1)^(n-k)*binomial(n,k)=(-1)^(n-k)*A007318(n,k) .
%e A130595 Triangle begins:
%e A130595 1;
%e A130595 -1, 1;
%e A130595 1, -2, 1;
%e A130595 -1, 3, -3, 1;
%e A130595 1, -4, 6, -4, 1;
%e A130595 -1, 5, -10, 10, -5, 1;
%e A130595 1, -6, 15, -20, 15, -6, 1;
%e A130595 -1, 7, -21, 35, -35, 21, -7, 1;
%e A130595 1, -8, 28, -56, 70, -56, 28, -8, 1;
%e A130595 -1, 9, -36, 84, -126, 126, -84, 36, -9, 1 ;...
%e A130595 Contribution from Peter Luschny (peter(AT)luschny.de), Jul 13 2009: (Start)
%e A130595 + 1
%e A130595 - 1 + 1 x
%e A130595 + 1 - 2 x + 1 x^2
%e A130595 - 1 + 3 x - 3 x^2 + 1 x^3
%e A130595 + 1 - 4 x + 6 x^2 - 4 x^3 + 1 x^4 (End)
%p A130595 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
%Y A130595 Sequence in context: A118433 A007318 A108086 this_sequence A108363 A076831 
               A119724
%Y A130595 Adjacent sequences: A130592 A130593 A130594 this_sequence A130596 A130597 
               A130598
%K A130595 sign,tabl,new
%O A130595 0,5
%A A130595 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 17 2007

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