A141680 Triangle read by rows: T(n,m) = (n/m)*binomial(n,m) if m divides n, otherwise 0.

1, 4, 1, 9, 0, 1, 16, 12, 0, 1, 25, 0, 0, 0, 1, 36, 45, 40, 0, 0, 1, 49, 0, 0, 0, 0, 0, 1, 64, 112, 0, 140, 0, 0, 0, 1, 81, 0, 252, 0, 0, 0, 0, 0, 1, 100, 225, 0, 0, 504, 0, 0, 0, 0, 1

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 07 2008

Keywords

• nonn
• tabl

Comments

Row sums are: 1, 5, 10, 29, 26, 122, 50, 317, 334, 830, ... A105862.

Examples

			1;
4, 1;
9, 0, 1;
16, 12, 0, 1;
25, 0, 0, 0, 1;
36, 45, 40, 0, 0, 1;
49, 0, 0, 0, 0, 0, 1;
64, 112, 0, 140, 0, 0, 0, 1;
81, 0, 252, 0, 0, 0, 0, 0, 1;
100, 225, 0, 0, 504, 0, 0, 0, 0, 1;
		

Links

• G. C. Greubel, Rows n=1..100 of triangle, flattened

Crossrefs

Cf. A015237, A105862, A126988.

Programs

Mathematica

t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]*Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]

Formula

T(n,m) = A126988(n,m)*binomial(n,m).

T(n,1) = n^2. T(n,n) = 1. T(2n,2) = A015237(n).