A132787 Triangle read by rows: T(n,k) = 2*A001263(n,k) - 1.

1, 1, 1, 1, 5, 1, 1, 11, 11, 1, 1, 19, 39, 19, 1, 1, 29, 99, 99, 29, 1, 1, 41, 209, 349, 209, 41, 1, 1, 55, 391, 979, 979, 391, 55, 1, 1, 71, 671, 2351, 3527, 2351, 671, 71, 1, 1, 89, 1079, 5039, 10583, 10583, 5039, 1079, 89, 1, 1, 109, 1649, 9899, 27719, 38807, 27719, 9899, 1649, 109, 1

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

Formula

Equals 2*A001263 - A000012 as infinite lower triangular matrices; where A001263 = the Narayana triangle.

T(n,k) = 2*binomial(n-1, k-1) * binomial(n, k-1) / k - 1. - Andrew Howroyd, Aug 10 2018

Example

First few rows of the triangle are:
  1;
  1, 1;
  1, 5, 1;
  1, 11, 11, 1;
  1, 19, 39, 19, 1;
  1, 29, 99, 99, 29, 1;
  ...

Prog

(PARI) T(n, k) = if(k<=n, 2*binomial(n-1, k-1) * binomial(n, k-1) / k - 1, 0); \\ Andrew Howroyd, Aug 10 2018

Crossrefs

Column 2 is A018387.

Row sums are A132788.

Cf. A001263.

Sequence in context: A173046 A173043 A082046 * A181370 A119307 A296039

Adjacent sequences: A132784 A132785 A132786 * A132788 A132789 A132790

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 30 2007

Extensions

a(20) corrected and terms a(56) and beyond from Andrew Howroyd, Aug 10 2018

Status

approved