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A104984
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Matrix inverse of triangle A104980.
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3
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1, -1, 1, -1, -2, 1, -3, -1, -3, 1, -13, -3, -1, -4, 1, -71, -13, -3, -1, -5, 1, -461, -71, -13, -3, -1, -6, 1, -3447, -461, -71, -13, -3, -1, -7, 1, -29093, -3447, -461, -71, -13, -3, -1, -8, 1, -273343, -29093, -3447, -461, -71, -13, -3, -1, -9, 1, -2829325, -273343, -29093, -3447, -461, -71, -13, -3, -1, -10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Inverse matrix A104980 satisfies: SHIFT_LEFT(column 0 of A104980^p) = p*(column p+1 of A104980) for p>=0.
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FORMULA
| T(n, n) = 1, T(n+1, n) = -(n+1) for n>=0; else T(n, k) = T(n-k, 0) = -A003319(n-k-1) for n>k+1 and k>=0.
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EXAMPLE
| Triangle begins:
1;
-1,1;
-1,-2,1;
-3,-1,-3,1;
-13,-3,-1,-4,1;
-71,-13,-3,-1,-5,1;
-461,-71,-13,-3,-1,-6,1;
-3447,-461,-71,-13,-3,-1,-7,1;
-29093,-3447,-461,-71,-13,-3,-1,-8,1; ...
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PROG
| (PARI) T(n, k)=if(n==k, 1, if(n==k+1, -n, -(n-k)!-sum(i=1, n-k-1, i!*T(n-k-i, 0))))
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CROSSREFS
| Cf. A104980.
Sequence in context: A134460 A130158 A187497 * A083868 A128199 A191350
Adjacent sequences: A104981 A104982 A104983 * A104985 A104986 A104987
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KEYWORD
| sign,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2005
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