A168404 E.g.f.: Sum_{n>=0} tan(2^n*x)^n/n!.

1, 2, 16, 528, 67584, 34210304, 69391122432, 565356426987520, 18478277930015260672, 2419401354886413876592640, 1267940756758206239694099841024, 2658665157828553829995392867121496064

Offset: 0

Author

Paul D. Hanna, Nov 25 2009

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 528*x^3/3! + 67584*x^4/4! +...
A(x) = 1 + tan(2*x) + tan(4*x)^2/2! + tan(8*x)^3/3! + tan(16*x)^4/4! +...+ tan(2^n*x)^n/n! +...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(tan(x)):
G(x) = 1 + x + x^2/2! + 3*x^3/3! + 9*x^4/4! + 37*x^5/5! + 177*x^6/6! +...+ A006229(n)*x^n/n! +...
		

Crossrefs

Cf. A006229 (exp(tan x)), variants: A136632, A168402, A168403, A168405, A168406, A168407, A168408.

Programs

PARI

{a(n)=n!*polcoeff(sum(k=0,n,tan(2^k*x +x*O(x^n))^k/k!),n)}

PARI

{a(n)=n!*polcoeff(exp(2^n*tan(x +x*O(x^n))),n)}

Formula

a(n) = [x^n/n! ] exp(2^n*tan(x)) for n>=0.