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A293991
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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_{j=1..k+1} binomial(k,j-1)*x^j/j).
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9
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 1, 1, 1, 4, 9, 10, 1, 1, 1, 5, 16, 33, 26, 1, 1, 1, 6, 25, 76, 141, 76, 1, 1, 1, 7, 36, 145, 436, 651, 232, 1, 1, 1, 8, 49, 246, 1025, 2776, 3333, 764, 1, 1, 1, 9, 64, 385, 2046, 8245, 19384, 18369, 2620, 1, 1, 1, 10, 81
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OFFSET
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0,9
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LINKS
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FORMULA
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E.g.f. of column k: exp(((1+x)^(k+1) - 1)/(k+1)).
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(k+1,n)} binomial(k,j-1)*A(n-j,k)/(n-j)! for n > 0.
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EXAMPLE
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Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, ...
1, 4, 9, 16, 25, ...
1, 10, 33, 76, 145, ...
1, 26, 141, 436, 1025, ...
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MATHEMATICA
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A[0, _] = 1; A[n_, k_] := (n-1)!*Sum[Binomial[k, j-1]*A[n-j, k]/(n-j)!, {j, 1, Min[k+1, n]}];
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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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