A127097 Triangle T(n,m) = A127093 * A126988 read by rows.

1, 5, 2, 10, 0, 3, 21, 10, 0, 4, 26, 0, 0, 0, 5, 50, 20, 15, 0, 0, 6, 50, 0, 0, 0, 0, 0, 7, 85, 42, 0, 20, 0, 0, 0, 8, 91, 0, 30, 0, 0, 0, 0, 0, 9, 130, 52, 0, 0, 25, 0, 0, 0, 0, 10, 122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 210, 100, 63, 40, 0, 30, 0, 0, 0, 0, 0, 12, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Gary W. Adamson, Jan 05 2007

Keywords

• nonn
• tabl

Comments

Multiply the infinite lower triangular matrices A127093 and A126988.

Examples

			First few rows of the triangle are:
1;
5, 2;
10, 0, 3;
21, 10, 0, 4;
26, 0, 0, 0, 5;
50, 20, 15, 0, 0, 6;
50, 0, 0, 0, 0, 0, 7;
...
		

Crossrefs

Cf. A126988, A000203, A127098, A001187, A001001 (row sums), A127093.

Programs

Maple

A127093 := proc(n,m) if n mod m = 0 then m; else 0 ; fi; end:
A126988 := proc(n,k) if n mod k = 0 then n/k; else 0; fi; end:
A127097 := proc(n,m) add( A127093(n,j)*A126988(j,m),j=m..n) ; end:
for n from 1 to 15 do for m from 1 to n do printf("%d,",A127097(n,m)) ; od: od: # R. J. Mathar, Aug 18 2009

Formula

T(n,m) = sum_{j=m..n} A127093(n,j)*A126988(j,m).

T(n,1) = A001157(n).

Extensions

A-numbers corrected by R. J. Mathar, Aug 18 2009