A194027 E.g.f.: Sum_{n>=0} sin(2^n*x)^n / 2^(n^2).

1, 1, 2, 2, -104, -3704, -113968, -2059408, 362847616, 113325214336, 25903723142912, 3643199606296832, -2713129993221899264, -5529958919819578778624, -7506437411940645017540608, -6418592915828033819245078528, 20775854326350479088039843168256

Offset

0,3

Comments

Signs of terms are of period 8: [+,+,+,+,-,-,-,-].

Links

Table of n, a(n) for n=0..16.

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

Cf. A194026.

Sequence in context: A270591 A210467 A156524 * A003110 A100956 A358621

Adjacent sequences: A194024 A194025 A194026 * A194028 A194029 A194030

Keyword

sign

Author

Paul D. Hanna, Aug 12 2011

Status

approved