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A293051
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{i=0..k} x^i/i! - exp(x)).
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6
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1, 1, -1, 1, 0, 0, 1, 0, -1, 1, 1, 0, 0, -1, 1, 1, 0, 0, -1, 2, -2, 1, 0, 0, 0, -1, 9, -9, 1, 0, 0, 0, -1, -1, 9, -9, 1, 0, 0, 0, 0, -1, 9, -50, 50, 1, 0, 0, 0, 0, -1, -1, 34, -267, 267, 1, 0, 0, 0, 0, 0, -1, -1, 90, -413, 413, 1, 0, 0, 0, 0, 0, -1, -1, 34, -71
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OFFSET
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0,20
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LINKS
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FORMULA
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E.g.f. of column k: Product_{i>k} exp(-x^i/i!).
A(0,k) = 1, A(1,k) = A(2,k) = ... = A(k,k) = 0 and A(n,k) = - Sum_{i=k..n-1} binomial(n-1,i)*A(n-1-i,k) for n > k.
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, ...
-1, 0, 0, 0, 0, ...
0, -1, 0, 0, 0, ...
1, -1, -1, 0, 0, ...
1, 2, -1, -1, 0, ...
-2, 9, -1, -1, -1, ...
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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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