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A129867
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Row sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
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5
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1, 2, 5, 14, 47, 200, 1073, 6986, 53219, 462332, 4500245, 48454958, 571411271, 7321388384, 101249656697, 1502852293010, 23827244817323, 401839065437636, 7182224591785949, 135607710526966262, 2696935204638786575
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OFFSET
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1,2
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COMMENTS
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First differences are 1, 3, 9, 33, 153, 873, 5913, ... (see A007489), second differences are 2, 6, 24, 120, 720, 5040, ... (see A000142 ).
First terms of the sequences of m-th differences are 1, 2, 4, 14, 64, ... (see A055790, A047920, A068106).
Antidiagonal sums are 1, 1, 3, 8, 29, 135, ... (see A130470) with first differences 0, 2, 5, 21, 106, ... (see A130471).
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LINKS
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EXAMPLE
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First seven rows of T are
[ 1 ]
[ 1, 1 ]
[ 2, 2, 1 ]
[ 6, 4, 3, 1 ]
[ 24, 12, 6, 4, 1 ]
[ 120, 48, 18, 8, 5, 1 ]
[ 720, 240, 72, 24, 10, 6, 1 ]
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PROG
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(Magma) m:=21; [ &+([ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]): j in [1..m] ]; // Klaus Brockhaus, May 28 2007
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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