A162507 Triangle read by rows, finite differences of an array generated by an infinite product (Cf. A162506).

1, 2, 1, 2, 3, 1, 4, 3, 4, 1, 4, 9, 4, 5, 1, 6, 12, 12, 5, 6, 1, 6, 18, 24, 15, 6, 7, 1, 8, 24, 36, 30, 18, 7, 8, 1, 8, 33, 60, 60, 36, 21, 8, 9, 1, 10, 39, 88, 95, 72, 42, 24, 9, 10, 1, 10, 51, 124, 160, 138, 84, 48, 27, 10, 11

Offset: 2

Author

Gary W. Adamson, Jul 04 2009

Keywords

• nonn
• tabl

Comments

Row sums = A162506 starting (1, 3, 6, 12, 23, 42, 77,...).

Examples

			The array =
1,...1,...1,...1,...1,...; = a
1,...1,...3,...3,...5,...; = a*b
1,...1,...3,...6,...8,...; = a*b*c
1,...1,...3,...6,..12,...; = a*b*c*d
...
taking finite differences from the top, then discarding the first "1",
we obtain triangle A162507:
1;
1, 2;
1, 2, 3;
1, 4, 3, 4;
1, 4, 9, 4, 5;
1, 6, 12, 12, 5, 6;
1, 6, 18, 24, 15, 6, 7;
1, 8, 24, 36, 30, 18, 7, 8;
1, 8, 33, 60, 60, 36, 21, 8, 9;
1, 10, 39, 88, 95, 72, 42, 24, 9, 10;
1, 10, 51, 124, 160, 138, 84, 48, 27, 10, 11;
...
		

Crossrefs

Cf. A162506.

Formula

Given the infinite product and array shown in A162506, we have

a = [1,1,1,...], b = [1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...];

The array is a, a*b, a*b*c,... Finite differences of array columns = rows of the triangle, deleting the first "1".