OFFSET
2,2
COMMENTS
Row sums = A162506 starting (1, 3, 6, 12, 23, 42, 77,...).
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".
EXAMPLE
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
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jul 04 2009
STATUS
approved