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Search: id:A129867
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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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+0
4
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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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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T read by rows is in A130469.
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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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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PROGRAM
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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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Cf. A130469, A007489, A000142, A055790, A047920, A068106, A130470, A130471.
Sequence in context: A007268 A109156 A143918 this_sequence A119841 A149905 A149906
Adjacent sequences: A129864 A129865 A129866 this_sequence A129868 A129869 A129870
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 24 2007
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 28 2007
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