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A362125
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Square array T(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of 1/(1 - x*(1+x)^k)^k.
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1
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1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 7, 3, 0, 1, 4, 15, 18, 5, 0, 1, 5, 26, 55, 47, 8, 0, 1, 6, 40, 124, 198, 118, 13, 0, 1, 7, 57, 235, 571, 681, 290, 21, 0, 1, 8, 77, 398, 1320, 2500, 2263, 702, 34, 0, 1, 9, 100, 623, 2640, 7026, 10504, 7341, 1677, 55, 0
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OFFSET
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0,8
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LINKS
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FORMULA
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T(n,k) = Sum_{j=0..n} (-1)^j * binomial(-k,j) * binomial(k*j,n-j) = Sum_{j=0..n} binomial(j+k-1,j) * binomial(k*j,n-j).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 2, 7, 15, 26, 40, ...
0, 3, 18, 55, 124, 235, ...
0, 5, 47, 198, 571, 1320, ...
0, 8, 118, 681, 2500, 7026, ...
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PROG
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(PARI) T(n, k) = sum(j=0, n, binomial(j+k-1, j)*binomial(k*j, n-j));
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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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