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A121438
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Matrix inverse of triangle A122178, where A122178(n,k) = C( n*(n+1)/2 + n-k - 1, n-k) for n>=k>=0.
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4
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1, -1, 1, -3, -3, 1, -17, -3, -6, 1, -160, -25, 5, -10, 1, -2088, -285, -35, 30, -15, 1, -34307, -4179, -420, -91, 84, -21, 1, -675091, -74823, -6916, -497, -322, 182, -28, 1, -15428619, -1577763, -135639, -10080, -63, -1002, 342, -36, 1, -400928675, -38209725, -3082905, -215700, -14139, 2655, -2625
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| A triangle having similar properties and complementary construction is the dual triangle A121434.
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FORMULA
| T(n,k) = [A121412^(-n*(n+1)/2)](n,k) for n>=k>=0; i.e., row n of A122178^-1 equals row n of matrix power A121412^(-n*(n+1)/2).
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EXAMPLE
| Triangle, A122178^-1, begins:
1;
-1, 1;
-3, -3, 1;
-17, -3, -6, 1;
-160, -25, 5, -10, 1;
-2088, -285, -35, 30, -15, 1;
-34307, -4179, -420, -91, 84, -21, 1;
-675091, -74823, -6916, -497, -322, 182, -28, 1;
-15428619, -1577763, -135639, -10080, -63, -1002, 342, -36, 1; ...
Triangle A121412 begins:
1;
1, 1;
3, 1, 1;
18, 4, 1, 1;
170, 30, 5, 1, 1; ...
Row 3 of A122178^-1 equals row 3 of A121412^(-6), which begins:
1;
-6, 1;
3, -6, 1;
-17, -3, -6, 1; ...
Row 4 of A122178^-1 equals row 4 of A121412^(-10), which begins:
1;
-10, 1;
25, -10, 1;
-15, 15, -10, 1;
-160, -25, 5, -10, 1; ...
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PROG
| (PARI) /* Matrix Inverse of A122178 */ {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(r*(r-1)/2+r-c-1, r-c)))); return((M^-1)[n+1, k+1])}
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CROSSREFS
| Cf. A122178 (matrix inverse); A121412; variants: A121439, A121440, A121441; A121434 (dual).
Sequence in context: A106210 A033842 A104417 * A108391 A111840 A174031
Adjacent sequences: A121435 A121436 A121437 * A121439 A121440 A121441
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KEYWORD
| sign,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 29 2006
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