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A106180
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Matrix inverse of number triangle A046854.
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6
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1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 0, 2, -2, -1, 1, -2, 2, 3, -3, -1, 1, 0, -5, 5, 4, -4, -1, 1, 5, -5, -9, 9, 5, -5, -1, 1, 0, 14, -14, -14, 14, 6, -6, -1, 1, -14, 14, 28, -28, -20, 20, 7, -7, -1, 1, 0, -42, 42, 48, -48, -27, 27
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| First column is A105523; second column is A106181.
Triangle T(n,k), 0<=k<=n, read by rows given by [ -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 29 2006
A124448*A007318 as infinite lower triangular matrices . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2007
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FORMULA
| Riordan array (1-y, y) where y=-(1-sqrt(1+4x^2))/(2x)
Sum_{k, 0<=k<=n} abs(T(n,k))=A063886(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 06 2006
T(0,0)=1 ; T(n,k)=0 if k<0 or if k>n ; T(n,0)=-T(n-1,0)-T(n-1,1) ; T(n,k)=T(n,k-1)-T(n-1,k+1) for k>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 27 2007
T(2n,0)=A000007(n) ; T(2n+2,2k+2)=-T(2n+2,2k+1)=(-1)^(n-k)*A039598(n,k) ; T(2n+1,2k+1)=-T(2n+1,2k)=(-1)^(n-k)*A039599(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
Sum_{k, k>=0} T(m,k)*T(n,k)*(-1)^k = T(m+n,0) = A105523(m+n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 24 2010]
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EXAMPLE
| Triangle begins
1;
-1,1;
0,-1,1;
1,-1,-1,1;
0,2,-2,-1,1;
-2,2,3,-3,-1,1;
0,-5,5,4,-4,-1,1;
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CROSSREFS
| Cf. A000108.
Sequence in context: A153864 A112399 A165123 * A055091 A014678 A164516
Adjacent sequences: A106177 A106178 A106179 * A106181 A106182 A106183
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 24 2005
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