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A360753
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Matrix inverse of A360657.
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1
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1, 0, 1, 0, -2, 1, 0, 1, -5, 1, 0, 1, 8, -9, 1, 0, 2, 4, 29, -14, 1, 0, 6, 4, -10, 75, -20, 1, 0, 24, 4, -41, -115, 160, -27, 1, 0, 120, -8, -147, -196, -490, 301, -35, 1, 0, 720, -136, -624, -392, -231, -1484, 518, -44, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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Conjectured formulas:
3. E.g.f. of column k > 0: Sum_{n >= k} T(n, k) * t^(n-1) / (n-1)! = (1 - t) * (Sum_{n >= k} A354795(n, k) * t^(n-1) / (n-1)!).
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EXAMPLE
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Triangle T(n, k) for 0 <= k <= n starts:
n\k : 0 1 2 3 4 5 6 7 8 9
=========================================================
0 : 1
1 : 0 1
2 : 0 -2 1
3 : 0 1 -5 1
4 : 0 1 8 -9 1
5 : 0 2 4 29 -14 1
6 : 0 6 4 -10 75 -20 1
7 : 0 24 4 -41 -115 160 -27 1
8 : 0 120 -8 -147 -196 -490 301 -35 1
9 : 0 720 -136 -624 -392 -231 -1484 518 -44 1
etc.
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PROG
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(PARI) tabl(m) = {my(n=2*m, A = matid(n), B, C, T); for( i = 2, n, for( j = 2, i, A[i, j] = A[i-1, j-1] + j * A[i-1, j] ) ); B = A^(-1); C = matrix( m, m, i, j, if( j == 1, 0^(i-1), sum( r = 0, i-j, B[i-j+1, r+1] * A[i-1+r, i-1] ) ) ); T = 1/C; }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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