A131250 A007318 * A004070.

1, 2, 1, 4, 4, 1, 8, 11, 6, 1, 16, 26, 22, 8, 1, 32, 57, 64, 37, 10, 1, 64, 120, 163, 130, 56, 12, 1, 128, 247, 382, 386, 232, 79, 14, 1, 256, 502, 848, 1024, 794, 378, 106, 16, 1, 512, 1013, 1816, 2510, 2380, 1471, 576, 137, 18, 1

Offset

0,2

Comments

Row sums = A061667: (1, 3, 9, 26, 73, 201, ...).

Companion triangle = A131249 = A007318 * A052509, where A052509 is the reversal of A004070.

Reversal of A097750. - Philippe Deléham, Jan 11 2014

Riordan array (1/(1-2x), x/(1-x)^2). - Philippe Deléham, Jan 11 2014

Diagonal sums are A045623. - Philippe Deléham, Jan 11 2014

Links

Table of n, a(n) for n=0..54.

Filippo Disanto, Some Statistics on the Hypercubes of Catalan Permutations, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.2 (see Table 2).

Formula

Binomial transform of A004070.

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0)=1, T(n,k)=0 if k < 0 or if k > n. - Philippe Deléham, Jan 11 2014

Example

First few rows of the triangle:
   1;
   2,  1;
   4,  4,  1;
   8, 11,  6,  1;
  16, 26, 22,  8,  1;
  32, 57, 64, 37, 10,  1;
  ...

Crossrefs

Cf. A004070, A061667, A131249, A007318.

Sequence in context: A122438 A350122 A156708 * A140693 A131249 A048807

Adjacent sequences: A131247 A131248 A131249 * A131251 A131252 A131253

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 23 2007

Extensions

More terms from Philippe Deléham, Jan 11 2014

Status

approved