1,2

First column is C(2n,n) or A000984. Central coefficients are C(3n,n) or A005809. [From Paul Barry (pbarry(AT)wit.ie), Oct 14 2009]

V. J. W. Guo and J. Zeng, The number of convex polyominoes and the generating function of Jacobi polynomials, Lemma 4.

As a number triangle, this is T(n, k)=if(k<=n, C(2n-k, n), 0). Its row sums are C(2n+1, n+1)=A001700. Its diagonal sums are A105872. - Paul Barry (pbarry(AT)wit.ie), Apr 23 2005

G.f.: 2^k/[sqrt(1-4x)*(1+sqrt(1-4x))^k].

As a number triangle, this is the Riordan array (1/sqrt(1-4x), xc(x)), c(x) the g.f. of A000108. - Paul Barry (pbarry(AT)wit.ie), Jun 24 2005

Contribution from Paul Barry (pbarry(AT)wit.ie), Oct 14 2009: (Start)

Triangle begins

1,

2, 1,

6, 3, 1,

20, 10, 4, 1,

70, 35, 15, 5, 1,

252, 126, 56, 21, 6, 1,

924, 462, 210, 84, 28, 7, 1,

3432, 1716, 792, 330, 120, 36, 8, 1

Production array is

2, 1,

2, 1, 1,

2, 1, 1, 1,

2, 1, 1, 1, 1,

2, 1, 1, 1, 1, 1,

2, 1, 1, 1, 1, 1, 1,

2, 1, 1, 1, 1, 1, 1, 1,

2, 1, 1, 1, 1, 1, 1, 1, 1,

2, 1, 1, 1, 1, 1, 1, 1, 1, 1 (End)

Rows 0-14 are A000984, A001700, A001791, A002054, A002694, A003516, A002696, A030053, A004310, A030054, A004311, A030055, A004312, A030056, A004313.

Columns are A000217, A000292, A000332, A000389, A000579.

Diagonals are A005809, A045721, A025174, A004319, A013698, A003408.

Sequence in context: A059300 A046803 A121468 this_sequence A128741 A060539 A163269

Adjacent sequences: A092389 A092390 A092391 this_sequence A092393 A092394 A092395

nonn,tabl

Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 21 2004