A131792 Main diagonal of triangle A131791: a(n) = A131791(n,n) for n>=0.

1, 1, 2, 6, 21, 76, 280, 1045, 3936, 14925, 56892, 217791, 836706, 3224157, 12456225, 48232162, 187131664, 727309265, 2831193004, 11036424667, 43076087806, 168322335246, 658416150496, 2577945422410, 10102468839284, 39621592646545

Offset: 0

Author

Paul D. Hanna, Jul 15 2007

Keywords

• nonn

Comments

Row n of triangle A131791 has 2^n terms for n>=0, where row sums and central terms of A131791 equals A028361: Product_{i=0..n-1} (2^i + 1).

Programs

PARI

{a(n)=if(n==0,1,polcoeff(prod(j=0,n-1,(1-x^(2^j+1))/(1-x)+x*O(x^n)),n))} \\ Max Alekseyev, Aug 30 2007

PARI

{T(n,k)=if(n==0,1,polcoeff(prod(j=0,n-1,(1-x^min(2^j+1,k+1))/(1-x)+x*O(x^k)),k))} \\ Martin Fuller, Aug 31 2007

Formula

a(n) = [x^n] Product_{j=0..n-1} [ (1 - x^(2^j+1) ) / (1-x) ] for n>0, with a(0)=1. - Max Alekseyev, Aug 30 2007.

Extensions

More terms from Max Alekseyev, Aug 30 2007.