A130303 A130296 * A000012.

1, 3, 1, 5, 2, 1, 7, 3, 2, 1, 9, 4, 3, 2, 1, 11, 5, 4, 3, 2, 1, 13, 6, 5, 4, 3, 2, 1, 15, 7, 6, 5, 4, 3, 2, 1, 17, 8, 7, 6, 5, 4, 3, 2, 1, 19, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Author

Gary W. Adamson, May 20 2007

Keywords

• nonn
• tabl

Examples

			1;
3, 1;
5, 2, 1;
7, 3, 2, 1;
9, 4, 3, 2, 1;
11, 5, 4, 3, 2, 1;
13, 6, 5, 4, 3, 2, 1;
15, 7, 6, 5, 4, 3, 2, 1;
17, 8, 7, 6, 5, 4, 3, 2, 1;
19, 9, 8, 7, 6, 5, 4, 3, 2, 1;
		

References

• H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162

Crossrefs

Cf. A130296, A000012, A034856 (row sums), A130302 (commuted matrix product)

Programs

Mathematica

Clear[e, n, k];
e[n_, 0] := 2*n - 1;
e[n_, k_] := 0 /; k >= n;
e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];
Table[Table[e[n, k], {k, 0, n - 1}], {n, 1, 10}];
Flatten[%]

Formula

A130296 * A000012 as infinite lower triangular matrices. (1,3,5,...) as the left border; (1,2,3,...) in all other columns.

e(n,k)= (e(n - 1, k)*e(n, k - 1) + 1)/e(n - 1, k - 1)

Extensions

Additional comments from Roger L. Bagula and Gary W. Adamson, Mar 28 2009