A194456 E.g.f.: Sum_{n>=0} 2^(-n*(n+1)/2!) * Product_{k=0..n} tan(2^k*x).

1, 2, 8, 64, 976, 23072, 808688, 48448384, 5085859456, 787587828992, 172251228685568, 61567677411810304, 37205957567375604736, 32218626571889542694912, 38411427146174647342235648, 73187646662485142233440845824, 231273043503438376340776532770816

Offset

1,2

Comments

Limit a(n)*a(n+2)/a(n+1)^2 appears to have 4 attractors near [1.33088873225, 1.28507876546, 1.49830439017, 1.56094802901]. [Extended by Vaclav Kotesovec, Oct 03 2020]

Limit ( a(n)*a(n+5)/(a(n+1)*a(n+4)) )^(1/4) appears to converge (1.41...?).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..106

Formula

E.g.f.: Sum_{n>=0} sin(x)^(n+1) * Product_{k=0..n} cos(2^k*x)^(n-1-k).

Example

E.g.f.: A(x) = x + 2*x^2/2! + 8*x^3/3! + 64*x^4/4! + 976*x^5/5! +...
where
A(x) = tan(x) + tan(x)*tan(2*x)/2 + tan(x)*tan(2*x)*tan(4*x)/2^3 + tan(x)*tan(2*x)*tan(4*x)*tan(8*x)/2^6 +...
A(x) = sin(x)/cos(x) + sin(x)^2/cos(2*x) + sin(x)^3*cos(x)/cos(4*x) + sin(x)^4*cos(x)^2*cos(2*x)/cos(8*x) + sin(x)^5*cos(x)^3*cos(2*x)^2*cos(4*x)/cos(16*x) + sin(x)^6*cos(x)^4*cos(2*x)^3*cos(4*x)^2*cos(8*x)/cos(32*x) +...

Prog

(PARI) {a(n)=local(A=sum(m=0, n, 2^(-m*(m+1)/2!)*prod(k=0, m, tan(2^k*x+x*O(x^n))))); n!*polcoeff(A, n)}
(PARI) {a(n)=local(X=x+x*O(x^n), A=sum(m=0, n, sin(X)^(m+1)*prod(k=0, m, cos(2^k*X)^(m-1-k)))); n!*polcoeff(A, n)}

Crossrefs

Cf. A194457, A194026, A194027.

Sequence in context: A153532 A153561 A192413 * A153542 A153570 A153533

Adjacent sequences: A194453 A194454 A194455 * A194457 A194458 A194459

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2011

Status

approved