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A129867
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.
5
1, 2, 5, 14, 47, 200, 1073, 6986, 53219, 462332, 4500245, 48454958, 571411271, 7321388384, 101249656697, 1502852293010, 23827244817323, 401839065437636, 7182224591785949, 135607710526966262, 2696935204638786575
OFFSET
1,2
COMMENTS
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).
Equals the row sums of irregular triangle A182961. - Paul D. Hanna, Mar 05 2012
LINKS
EXAMPLE
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 ]
PROG
(Magma) m:=21; [ &+([ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]): j in [1..m] ]; // Klaus Brockhaus, May 28 2007
KEYWORD
nonn
AUTHOR
Paul Curtz, May 24 2007
EXTENSIONS
Edited and extended by Klaus Brockhaus, May 28 2007
STATUS
approved