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A080955
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Square array of numbers related to the incomplete gamma function, read by antidiagonals.
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7
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1, 1, 1, 1, 2, 2, 1, 3, 5, 6, 1, 4, 10, 16, 24, 1, 5, 17, 38, 65, 120, 1, 6, 26, 78, 168, 326, 720, 1, 7, 37, 142, 393, 872, 1957, 5040, 1, 8, 50, 236, 824, 2208, 5296, 13700, 40320, 1, 9, 65, 366, 1569, 5144, 13977, 37200, 109601, 362880, 1, 10, 82, 538, 2760, 10970, 34960, 100026
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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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T(k,n) = n! * Sum{j=0..n} k^j/j!.
E.g.f. of k-th row: exp(k*x)/(1-x).
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EXAMPLE
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Array begins:
k=0: 1 1 2 6 24 ...
k=1: 1 2 5 16 65 ...
k=2: 1 3 10 38 168 ...
k=3: 1 4 17 78 393 ...
k=4: 1 5 26 142 824 ...
...
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MATHEMATICA
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T[0, k_] := k!; T[n_, k_] := k!*Sum[n^j/j!, {j, 0, k}];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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