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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 (list; graph; refs; listen; history; text; internal format)
 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 Vincenzo Librandi, Table of n, a(n) for n = 1..100 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 CROSSREFS Cf. A130469, A007489, A000142, A055790, A047920, A068106, A130470, A130471. Cf. A182961. Sequence in context: A326898 A109156 A143918 * A119841 A149905 A149906 Adjacent sequences: A129864 A129865 A129866 * A129868 A129869 A129870 KEYWORD nonn AUTHOR Paul Curtz, May 24 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, May 28 2007 STATUS approved

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Last modified December 7 21:37 EST 2023. Contains 367662 sequences. (Running on oeis4.)