OFFSET
0,3
COMMENTS
Signs of terms are of period 8: [+,+,+,+,-,-,-,-].
FORMULA
E.g.f.: Sum_{n>=0} sin(x)^n * Product_{k=0..n-1} cos(2^k*x)^n.
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 2*x^3/3! - 104*x^4/4! - 3704*x^5/5! +...
where
A(x) = 1 + sin(2*x)/2 + sin(2^2*x)^2/2^4 + sin(2^3*x)^3/2^9 + sin(2^4*x)^4/2^16 +...
Also,
A(x) = 1 + sin(x)*cos(x) + sin(x)^2*cos(x)^2*cos(2*x)^2 + sin(x)^3*cos(x)^3*cos(2*x)^3*cos(4*x)^3 + sin(x)^4*cos(x)^4*cos(2*x)^4*cos(4*x)^4*cos(8*x)^4 +...
PROG
(PARI) {a(n)=local(X=x+x*O(x^n), A=sum(m=0, n, sin(2^m*X)^m/2^(m^2))); n!*polcoeff(A, n)}
(PARI) {a(n)=local(X=x+x*O(x^n), A=sum(m=0, n, sin(X)^m*prod(k=0, m-1, cos(2^k*X)^m))); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Aug 12 2011
STATUS
approved