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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.

%I A129867 #13 Sep 08 2022 08:45:30
%S A129867 1,2,5,14,47,200,1073,6986,53219,462332,4500245,48454958,571411271,
%T A129867 7321388384,101249656697,1502852293010,23827244817323,401839065437636,
%U A129867 7182224591785949,135607710526966262,2696935204638786575
%N 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.
%C A129867 T read by rows is in A130469.
%C A129867 First differences are 1, 3, 9, 33, 153, 873, 5913, ... (see A007489), second differences are 2, 6, 24, 120, 720, 5040, ... (see A000142 ).
%C A129867 First terms of the sequences of m-th differences are 1, 2, 4, 14, 64, ... (see A055790, A047920, A068106).
%C A129867 Antidiagonal sums are 1, 1, 3, 8, 29, 135, ... (see A130470) with first differences 0, 2, 5, 21, 106, ... (see A130471).
%C A129867 Equals the row sums of irregular triangle A182961. - _Paul D. Hanna_, Mar 05 2012
%H A129867 Vincenzo Librandi, <a href="/A129867/b129867.txt">Table of n, a(n) for n = 1..100</a>
%e A129867 First seven rows of T are
%e A129867 [   1 ]
%e A129867 [   1,   1 ]
%e A129867 [   2,   2,   1 ]
%e A129867 [   6,   4,   3,   1 ]
%e A129867 [  24,  12,   6,   4,   1 ]
%e A129867 [ 120,  48,  18,   8,   5,   1 ]
%e A129867 [ 720, 240,  72,  24,  10,   6,   1 ]
%o A129867 (Magma) m:=21; [ &+([ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]): j in [1..m] ]; // _Klaus Brockhaus_, May 28 2007
%Y A129867 Cf. A130469, A007489, A000142, A055790, A047920, A068106, A130470, A130471.
%Y A129867 Cf. A182961.
%K A129867 nonn
%O A129867 1,2
%A A129867 _Paul Curtz_, May 24 2007
%E A129867 Edited and extended by _Klaus Brockhaus_, May 28 2007