0,2

Array interpretation : first row is filled with 1's, first column with powers of 2, b(i,j)=b(i-1,j)+b(i,j-1); then a(n)=b(n,n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 01 2002

1 1 1 1 1 1 1 ...

2 3 4 5 6 7 8 ...

4 7 11 16 22 ....

8 15 26 42 64....

16 31 ..99 163...

Hankel transform is n+1. - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 27 2008: (Start)

A032443 is an analogue of the Catalan sequence: Let M = an infinite Cartan

matrix (-1's in the super and sub-diagonals and (2,2,2,...) in the main

diagonal which we modify to (1,2,2,2,...). Then A000108 can be generated by

accessing the leftmost term in M^n * [1,0,0,0,...]. Change the operation to M^n * [1,2,3,...] to get A032443. Or, take iterates M * [1,2,3,...] -> M * ANS, -> M * ANS,...; accessing the leftmost term. (End)

Convolved with the Catalan sequence, A000108: (1, 1, 2, 5, 14,...) = powers of 4, A000302: (1, 4, 16, 64,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 15 2009]

Row sums of A094527. [From Paul Barry (pbarry(AT)wit.ie), Sep 07 2009]

Hankel tranform of the aeration of this sequence is C(n+2,2). [From Paul Barry (pbarry(AT)wit.ie), Sep 26 2009]

A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, preprint, 2007.

M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.

(4^n+binomial(2*n, n))/2 (David W. Wilson)

a(n)=sum_{0<=i_1<=i_2<=n}binomial(n, i_2)*binomial(n, i_1+i_2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 14 2004

Sequence with interpolated zeros has a(n)=sum{k=0..floor(n/2), if(mod(n-2k, 2)=0, C(n, k), 0)}. - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005

a(n)=sum{k=0..n, C(n+k-1,k)2^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Sep 28 2007

Binomial transform of A027914. Hankel transform is {1, 2, 3, 4, ..., n, ...} - John W. Layman (layman(AT)math.vt.edu), Aug 04 2000

A000108 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 27 2008]

A000302 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 15 2009]

Sequence in context: A106460 A059716 A122368 this_sequence A143464 A117641 A084782

Adjacent sequences: A032440 A032441 A032442 this_sequence A032444 A032445 A032446

nonn

J. H. Conway (conway(AT)math.princeton.edu)