0,8

Contribution from Paul Barry (pbarry(AT)wit.ie), Nov 10 2008: (Start)

As number triangle, Riordan array (1, x(1-x)/(1-2x)). A062110*A007318 is A147703.

[0,1,1,0,0,0,....] DELTA [1,0,0,0,.....] (Deleham DELTA defined in A084938). (End)

Modulo 2, this sequence becomes A106344 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 18 2008]

T(n, k)=T(n-1, k)+sum{j<k}[T(n, j)] with T(0, k)=0^k.

G.f.: 1/(1-x(1-y)/(1-2y)) = Sum_{i, j} a(i, j)x^i*y^j.

T(n,k)=A121462(n+1,k+1)*2^(n-2*k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 01 2006

Sum_{k, 0<=k<=n}T(n,k)*x^k = A152239(n), A152223(n), A152185(n), A152174(n), A152167(n), A152166(n), A152163(n), A000007(n), A001519(n), A006012(n), A081704(n), A082761(n), A147837(n), A147838(n), A147839(n), A147840(n), A147841(n), for x = -7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9 respectively. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 09 2008]

Rows start (1,0,0,0,0,...), (1,1,2,4,8,...), (1,2,5,12,28,...), etc.

Triangle begins : 1 ; 0, 1 ; 0, 1, 1 ; 0, 2, 2, 1 ; 0, 4, 5, 3, 1 ; 0, 8, 12, 9, 4, 1 ; 0, 16, 28, 25, 14, 5, 1 ; 0, 32, 64, 66, 44, 20, 6, 1 ; 0, 64, 144, 168, 129, 70, 27, 7, 1 ; 0, 128, 320, 416, 360, 225, 104, 35, 8, 1 ;... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2008]

(PARI) a(i, j)=if(i<0|j<0, 0, polcoeff(((1-x)/(1-2*x)+x*O(x^j))^i, j))

Rows include A000007, A011782, A045623, A058396, A062109. Columns include A000012, A001477, A000096, A000297. Main diagonal is A002002. T(n, k) is a multiple of 2^(k-n), dividing by this gives a table similar to A050143 except at the edges.

Essentially the same array as A105306.

Sequence in context: A071510 A110124 A116389 this_sequence A122896 A107267 A112161

Adjacent sequences: A062107 A062108 A062109 this_sequence A062111 A062112 A062113

nonn,tabl

Henry Bottomley (se16(AT)btinternet.com), May 30 2001