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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
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OFFSET
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0,12
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COMMENTS
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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 Deléham, Sep 29 2006
A124448*A007318 as infinite lower triangular matrices. - Philippe Deléham, Oct 16 2007
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LINKS
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Table of n, a(n) for n=0..61.
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FORMULA
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Riordan array (1-y, y) where y=-(1-sqrt(1+4x^2))/(2x).
Sum_{k=0..n} abs(T(n,k)) = A063886(n). - Philippe Deléham, 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 Deléham, 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 Deléham, Oct 29 2007
Sum_{k>=0} T(m,k)*T(n,k)*(-1)^k = T(m+n,0) = A105523(m+n). - Philippe Deléham, Jan 24 2010
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EXAMPLE
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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
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Cf. A000108.
Sequence in context: A112399 A165123 A318439 * A274369 A055091 A332380
Adjacent sequences: A106177 A106178 A106179 * A106181 A106182 A106183
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry, Apr 24 2005
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STATUS
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approved
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