A117380 Riordan array (1/(1-4*x*c(x)),xc(x)), c(x) the g.f. of A000108.

1, 4, 1, 20, 5, 1, 104, 26, 6, 1, 548, 137, 33, 7, 1, 2904, 726, 178, 41, 8, 1, 15432, 3858, 954, 228, 50, 9, 1, 82128, 20532, 5100, 1242, 288, 60, 10, 1, 437444, 109361, 27233, 6701, 1601, 359, 71, 11, 1, 2331128, 582782, 145338, 35977, 8744, 2043, 442, 83, 12

Offset: 0

Author

Paul Barry, Mar 10 2006

Keywords

• easy
• nonn
• tabl

Comments

Triangle factors as (1,xc(x))*(1/(1-4x),x). Inverse of A117377. First row is A076035. Second row is A076025(n)-0^n. Row sums are A076025(n+1). Diagonal sums are A117381.

Examples

			Triangle begins
1,
4, 1,
20, 5, 1,
104, 26, 6, 1,
548, 137, 33, 7, 1,
2904, 726, 178, 41, 8, 1
Production array begins
4, 1
4, 1, 1
4, 1, 1, 1
4, 1, 1, 1, 1
4, 1, 1, 1, 1, 1
4, 1, 1, 1, 1, 1, 1
4, 1, 1, 1, 1, 1, 1, 1
4, 1, 1, 1, 1, 1, 1, 1, 1
... - _Philippe Deléham_, Mar 05 2013
		

Formula

Number triangle T(0,0)=1, T(n,k)=[k<=n]*sum{j=0..n, (j/(n-j))*C(2n-j,n-j)[k<=j]*4^(j-k)}