A136573 Triangle read by rows: (A000012 * A136572 + A136572 * A000012) - A000012.

1, 1, 1, 2, 2, 3, 6, 6, 7, 11, 24, 24, 25, 29, 47, 120, 120, 121, 125, 143, 239, 720, 720, 721, 725, 743, 839, 1439, 5040, 5040, 5041, 5045, 5063, 5159, 5759, 10079, 40320, 40320, 40321, 40325, 40343, 40439, 41039, 45359, 80639, 362880, 362880, 362881, 362885, 362903, 362999, 363599, 367919, 403199, 725759

Offset: 0

Author

Gary W. Adamson, Jan 07 2008

Keywords

• nonn
• tabl

Comments

Row sums = A136574.

Right border = 2*n! - 1 = A020543: (1, 1, 3, 11, 47, 239, 1439, ...).

Examples

			First few rows of the triangle:
     1;
     1,    1;
     2,    2,    3;
     6,    6,    7,   11;
    24,   24,   25,   49,   47;
   120,  120,  121,  125,  143,  239;
   720,  720,  721,  725,  743,  839, 1439;
  5040, 5040, 5041, 5045, 5063, 5159, 5759, 10079;  ...
Row 4 = (24, 24, 25, 29, 47) = 5 terms of (24, 24, 24, 24, 24) + (0, 0, 1, 5, 23), where A033312 = (0, 0, 1, 5, 23, 119, 719, 5039, ...).
		

Crossrefs

Cf. A020543, A033312, A136572, A136574.

Formula

(A000012 * A136572 + A136572 * A000012) - A000012, as infinite lower triangular matrices.

Triangle read by rows: n-th row = (n+1) terms of n! + (k! - 1), k = 0, 1, 2, ...; where the sequence (k! - 1) = A033312: (0, 0, 1, 5, 23, 119, 719, 5039, ...).

Extensions

a(41) corrected and more terms from Georg Fischer, Jun 05 2023