0,2

Right-hand side of even-numbered rows of Pascal's triangle.

Row sums are A032443. Reverse of A062344. Right-hand side of A034870. Binomial transform of trinomial triangle A094531.

Triangle T(n,k),0<=k<=n, read by rows defined by :T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,0)=2*T(n-1,0)+2*T(n-1,1), T(n,k)=T(n-1,k-1)+2*T(n-1,k)+T(n-1,k+1) for k>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 14 2007

Riordan array (1/sqrt(1-4x)), (1-2x-sqrt(1-4x))/(2x)). Column k has e.g.f. exp(2x)Bessel_I(k, 2x). - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005

Product of Product of Riordan arrays (1/(1-x), x/(1-x)) (Pascal's triangle, A007318) and (1/sqrt(1-2x-3x^2), (1-x-sqrt(1-2x-3x^2))/(2x)) (A094531). Inverse is A110162. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005

T(n,k)=sum{j=0..n, C(n,j)C(n,j-k)}. - Paul Barry (pbarry(AT)wit.ie), Mar 07 2006

T(n,k)= Sum_{h>=k}A039599(n,h) . Sum_{0<=k<=n}T(n,k)= A032443(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), May 01 2006

Sum_{k = 0...n}T(n,k)^2 = A036910(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), May 07 2006

Sum_{k, 0<=k<=n}T(n,k)*(-1)^k=A088218(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 14 2007

Triangle begins:

1;

2, 1;

6, 4, 1;

20, 15, 6, 1;

70, 56, 28, 8, 1;

252, 210, 120, 45, 10, 1;

924, 792, 495, 220, 66, 12, 1;

Cf. A007318, A032443, A039599.

Sequence in context: A118040 A073387 A125693 this_sequence A054335 A110681 A117852

Adjacent sequences: A094524 A094525 A094526 this_sequence A094528 A094529 A094530

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), May 07 2004

Entry revised by njas, Mar 23 2007