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

0,2

Links

Table of n, a(n) for n=0..13.

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! + ...

Example

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

Prog

(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]))}

Crossrefs

Cf. A098539, A111811.

Sequence in context: A013992 A279156 A129103 * A138433 A242597 A339469

Adjacent sequences: A111809 A111810 A111811 * A111813 A111814 A111815

Keyword

nonn

Author

Paul D. Hanna, Aug 22 2005

Status

approved