A111812 Column 3 of triangle A098539, which shifts columns left and up under matrix square.

1, 8, 72, 888, 16392, 479736, 23196168, 1909718520, 273790460424, 69532461669880, 31699923943776776, 26220200137673186808, 39689067731528646091272, 110732781183212424923225592

Offset: 0

Author

Paul D. Hanna, Aug 22 2005

Keywords

• nonn

Examples

			A(x) = 1 + 8*x + 72*x^2 + 888*x^3 + 16392*x^4 + 479736*x^5 +...
		

Crossrefs

Cf. A098539, A111811.

Programs

PARI

{a(n,q=2)=local(A=Mat(1),B);if(n<0,0, for(m=1,n+4,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=1,if(j==1,B[i,j]=(A^q)[i-1,1], B[i,j]=(A^q)[i-1,j-1]));));A=B);return(A[n+4,4]))}

Formula

G.f.: A(x) = 1 + Sum_{n>=1} 8^n/n!*Product_{j=0..n-1} L(2^j*x) where L(x) = e.g.f. of A111811 (column 0 of matrix log of A098539) satisfies: x = L(x) - L(x)*L(2*x)/2! + L(x)*L(2*x)*L(2^2*x)/3! - L(x)*L(2*x)*L(2^2*x)*L(2^3*x)/4! + ...