A140822 Triangle T(n,m) = binomial(n,gcd(n,m)) read by rows, 0<=m<=n.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 28, 8, 70, 8, 28, 8, 1, 1, 9, 9, 84, 9, 9, 84, 9, 9, 1, 1, 10, 45, 10, 45, 252, 45, 10, 45, 10, 1

Offset

0,5

Comments

Row sums are 1, 2, 4, 8, 16, 22, 64, 44, 160, 224, 474,...

Links

Table of n, a(n) for n=0..65.

Formula

T(n,m) = A007318(n,A109004(n,m)).

Example

1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 6, 4, 1;
1, 5, 5, 5, 5, 1;
1, 6, 15, 20, 15, 6, 1;
1, 7, 7, 7, 7, 7, 7, 1;
1, 8, 28, 8, 70, 8, 28, 8, 1;
1, 9, 9, 84, 9, 9, 84, 9, 9, 1;
1, 10, 45, 10, 45, 252, 45, 10, 45, 10, 1;

Mathematica

a = Table[Table[Binomial[n, GCD[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[a]

Crossrefs

Sequence in context: A034930 A095142 A180171 * A212954 A299807 A089239

Adjacent sequences: A140819 A140820 A140821 * A140823 A140824 A140825

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Gary W. Adamson, Jul 16 2008

Extensions

Offset corrected by R. J. Mathar, Nov 07 2011

Status

approved