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.

1, 2, 5, 14, 47, 200, 1073, 6986, 53219, 462332, 4500245, 48454958, 571411271, 7321388384, 101249656697, 1502852293010, 23827244817323, 401839065437636, 7182224591785949, 135607710526966262, 2696935204638786575

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