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Triangle read by rows: (A000012 * A136572 + A136572 * A000012) - A000012.
1

%I #9 Jun 05 2023 05:22:58

%S 1,1,1,2,2,3,6,6,7,11,24,24,25,29,47,120,120,121,125,143,239,720,720,

%T 721,725,743,839,1439,5040,5040,5041,5045,5063,5159,5759,10079,40320,

%U 40320,40321,40325,40343,40439,41039,45359,80639,362880,362880,362881,362885,362903,362999,363599,367919,403199,725759

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

%C Row sums = A136574.

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

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

%F 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, ...).

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 2, 2, 3;

%e 6, 6, 7, 11;

%e 24, 24, 25, 49, 47;

%e 120, 120, 121, 125, 143, 239;

%e 720, 720, 721, 725, 743, 839, 1439;

%e 5040, 5040, 5041, 5045, 5063, 5159, 5759, 10079; ...

%e 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, ...).

%Y Cf. A020543, A033312, A136572, A136574.

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Jan 07 2008

%E a(41) corrected and more terms from _Georg Fischer_, Jun 05 2023