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

1,2

Comments

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

Links

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

Formula

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

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

Example

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;

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[%]

Crossrefs

Cf. A015237, A105862, A126988.

Sequence in context: A036177 A360131 A177841 * A141681 A176215 A364016

Adjacent sequences: A141677 A141678 A141679 * A141681 A141682 A141683

Keyword

nonn,tabl

Author

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

Status

approved