OFFSET
0,3
COMMENTS
Let q=7; the g.f. of column k of A111830^m (matrix power m) is: 1 + Sum_{n>=1} (m*q^k)^n/n! * Product_{j=0..n-1} A(q^j*x).
FORMULA
E.g.f. satisfies: x/(1-x) = Sum_{n>=1} Prod_{j=0..n-1} A(7^j*x)/(j+1).
EXAMPLE
A(x) = x - 5/2!*x^2 + 83/3!*x^3 + 16110/4!*x^4 - 40097784/5!*x^5 +...
where e.g.f. A(x) satisfies:
x/(1-x) = A(x) + A(x)*A(7*x)/2! + A(x)*A(7*x)*A(7^2*x)/3! +
A(x)*A(7*x)*A(7^2*x)*A(7^3*x)/4! + ...
G(x) = 1 + 7*A(x) + 7^2*A(x)*A(7*x)/2! +
7^3*A(x)*A(7*x)*A(7^2*x)/3! +
7^4*A(x)*A(7*x)*A(7^2*x)*A(7^3*x)/4! + ...
PROG
(PARI) {a(n, q=7)=local(A=x/(1-x+x*O(x^n))); for(i=1, n, A=x/(1-x)/(1+sum(j=1, n, prod(k=1, j, subst(A, x, q^k*x))/(j+1)!))); return(n!*polcoeff(A, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Gottfried Helms and Paul D. Hanna, Aug 22 2005
STATUS
approved