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A132787
Triangle read by rows: T(n,k) = 2*A001263(n,k) - 1.
3
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
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