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A130469 Triangular array read by rows: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j. 4

%I

%S 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,

%T 5040,1440,360,96,30,12,7,1,40320,10080,2160,480,120,36,14,8,1,362880,

%U 80640,15120,2880,600,144,42,16,9,1,3628800,725760,120960,20160,3600

%N Triangular array read by rows: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.

%C T is also defined in A129867, which gives row sums of T.

%e First seven rows of T are

%e [ 1 ]

%e [ 1, 1 ]

%e [ 2, 2, 1 ]

%e [ 6, 4, 3, 1 ]

%e [ 24, 12, 6, 4, 1 ]

%e [ 120, 48, 18, 8, 5, 1 ]

%e [ 720, 240, 72, 24, 10, 6, 1 ]

%o (MAGMA) m:=11; &cat[ [ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]: j in [1..m] ];

%Y Cf. A129867, A130470 (antidiagonal sums), A130471 (first differences of antidiagonal sums).

%K nonn,tabl

%O 1,4

%A _Klaus Brockhaus_, May 28 2007

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Last modified January 20 12:26 EST 2022. Contains 350472 sequences. (Running on oeis4.)