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%I #12 Feb 18 2022 22:40:36

%S 1,2,1,3,3,1,4,6,3,1,5,10,7,3,1,6,15,14,7,3,1,7,21,25,15,7,3,1,8,28,

%T 41,30,15,7,3,1,9,36,63,56,31,15,7,3,1,10,45,92,98,62,31,15,7,3,1

%N A000012 * A052509.

%C Row sums = A001924: (1, 3, 7, 14, 26, 46, 79, ...). A131252 = A052509 * A000012.

%C From _Clark Kimberling_, Feb 07 2011: (Start)

%C When formatted as a rectangle R with northwest corner

%C 1, 2, 3, 4, 5, 6, ...

%C 1, 3, 6, 10, 15, 21, ...

%C 1, 3, 7, 14, 25, 41, ...

%C 1, 3, 7, 15, 30, 56, ...

%C 1, 3, 7, 15, 31, 62, ...

%C ...

%C the following properties hold:

%C R is the accumulation array of the transpose of A052553 (a version of Pascal's triangle); see A144112 for the definition of accumulation array.

%C row 1: A000027

%C row 2: A000217

%C row 3: A004006

%C row 4: A055795

%C row 5: A057703

%C row 6: A115567

%C limiting row: A000225

%C antidiagonal sums: A001924.

%C (End)

%F A000012 * A052509 as infinite lower triangular matrices.

%e First few rows of the triangle:

%e 1;

%e 2, 1;

%e 3, 3, 1;

%e 4, 6, 3, 1;

%e 5, 10, 7, 3, 1;

%e 6, 15, 14, 7, 3, 1;

%e 7, 21, 25, 15, 7, 3, 1;

%e ...

%Y Cf. A052509, A000012, A001924, A131252.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Jun 23 2007