OFFSET
0,3
FORMULA
Define F(x,k,m) = Sum_{n>=1} (m*2^k)^n/n! * Product_{j=0..n-1} A(2^j*x), then F(x,k,m) is a series in x with integer coefficients for all integer m, k>=0.
EXAMPLE
E.g.f.: A(x) = x + 2x^2/2! - 8x^3/3! - 80x^4/4! + 1576x^5/5! + 43056x^6/6! + ...
where A(x) satisfies:
x/(1-x)^2 = A(x) + A(x)*A(2*x)/2! + A(x)*A(2*x)*A(2^2*x)/3! + A(x)*A(2*x)*A(2^2*x)*A(2^3*x)/4! + ...
PROG
(PARI) {a(n, q=2)=local(A=x/(1-x+x*O(x^n))^2); for(i=1, n, A=x/(1-x)^2/(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
Paul D. Hanna, Nov 23 2007
STATUS
approved