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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

%I

%S 1,2,5,14,47,200,1073,6986,53219,462332,4500245,48454958,571411271,

%T 7321388384,101249656697,1502852293010,23827244817323,401839065437636,

%U 7182224591785949,135607710526966262,2696935204638786575

%N 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.

%C T read by rows is in A130469.

%C First differences are 1, 3, 9, 33, 153, 873, 5913, ... (see A007489), second differences are 2, 6, 24, 120, 720, 5040, ... (see A000142 ).

%C First terms of the sequences of m-th differences are 1, 2, 4, 14, 64, ... (see A055790, A047920, A068106).

%C Antidiagonal sums are 1, 1, 3, 8, 29, 135, ... (see A130470) with first differences 0, 2, 5, 21, 106, ... (see A130471).

%C Equals the row sums of irregular triangle A182961. - _Paul D. Hanna_, Mar 05 2012

%H Vincenzo Librandi, <a href="/A129867/b129867.txt">Table of n, a(n) for n = 1..100</a>

%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:=21; [ &+([ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]): j in [1..m] ]; // _Klaus Brockhaus_, May 28 2007

%Y Cf. A130469, A007489, A000142, A055790, A047920, A068106, A130470, A130471.

%Y Cf. A182961.

%K nonn

%O 1,2

%A _Paul Curtz_, May 24 2007

%E Edited and extended by _Klaus Brockhaus_, May 28 2007

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)