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A098435
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Triangle of Salie numbers T(n,k) for negative n,k, n < k.
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3
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1, -1, 1, 2, -3, 1, -8, 13, -6, 1, 56, -92, 45, -10, 1, -608, 1000, -493, 115, -15, 1, 9440, -15528, 7662, -1799, 245, -21, 1, -198272, 326144, -160944, 37817, -5180, 462, -28, 1, 5410688, -8900224, 4392080, -1032088, 141465, -12684, 798, -36, 1
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OFFSET
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1,4
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COMMENTS
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Inverse matrix of A054142. - Paul Barry, Jan 21 2005
Essentially the same as the triangle giving by [0,-1,-1,-4,-4,-9,-9,-16,-16,-25,...] DELTA[1,0,1,0,1,0,1,0,1,0,...] = 1; 0,1; 0,-1,1; 0,2,-3,1; 0,-8,13,-6,1; 0,56,-92,45,-10,1; ... where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 30 2006
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LINKS
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Table of n, a(n) for n=1..45.
D. Dumont and J. Zeng, Polynomes d'Euler et les fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998) 3, 387-410.
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FORMULA
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See A065547 for formulas.
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EXAMPLE
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1;
-1, 1;
2, -3, 1;
-8, 13, -6, 1;
56, -92, 45, -10, 1;
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MATHEMATICA
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rows = 9; A054142 = Table[ PadRight[ Table[ Binomial[2*n-k, k], {k, 0, n}], rows], {n, 0, rows-1}]; inv = Inverse[A054142]; Table[ Take[inv[[n]], n], {n, 1, rows}] // Flatten (* Jean-François Alcover, Oct 02 2013, after Paul Barry *)
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CROSSREFS
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T(-1, k) = (-1)^k*A005439(k-1). Row sums are zero.
Sequence in context: A110292 A138672 A103749 * A096294 A157963 A135950
Adjacent sequences: A098432 A098433 A098434 * A098436 A098437 A098438
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KEYWORD
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tabl,sign
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AUTHOR
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Ralf Stephan, Sep 08 2004
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STATUS
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approved
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