A102224 Column 0 of the matrix square of A102220, which equals the lower triangular matrix: [2*I - A008459]^(-1).

1, 2, 14, 200, 4814, 174752, 8909168, 606818060, 53211837134, 5838211285616, 783434682568664, 126221710572107900, 24043148814317769584, 5344827109234104188348, 1371307353540074156012828

Offset: 0

Author

Paul D. Hanna, Dec 31 2004

Keywords

• nonn

Comments

A102221 is column 0 of A102220.

Triangle A008459 consists of the squared binomial coefficients.

Examples

			Given A102221 = [1,1,5,55,1077,32951,1451723,87054773,...], then this sequence results from a type of self-convolution of A102221:
a(2) = 14 = 1^2*1*5 + 2^2*1*1 + 1^2*5*1,
a(3) = 200 = 1^2*1*55 + 3^2*1*5 + 3^2*5*1 + 1^2*55*1.
		

Crossrefs

Cf. A102220, A102221, A008459.

Programs

PARI

{a(n)=(matrix(n+1,n+1,i,j,if(i==j,2,0)-binomial(i-1,j-1)^2)^-2)[n+1,1]}

Formula

a(n) = Sum_{k=0..n} C(n, k)^2*A102221(k)*A102221(n-k).

Sum_{n>=0} a(n)*x^n/n!^2 = 1/(2-BesselI(0,2*sqrt(x)))^2. - Vladeta Jovovic, Jul 17 2006