

A129867


Row sums of triangular array T: T(j,k) = k*(jk)! 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
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OFFSET

1,2


COMMENTS

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 mth 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).


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(jk): k in [1..j1] ] cat [ 1 ]): j in [1..m] ]; // Klaus Brockhaus, May 28 2007


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



