A168404 - OEIS

%I #2 Mar 30 2012 18:37:20

%S 1,2,16,528,67584,34210304,69391122432,565356426987520,

%T 18478277930015260672,2419401354886413876592640,

%U 1267940756758206239694099841024,2658665157828553829995392867121496064

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

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

%e E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 528*x^3/3! + 67584*x^4/4! +...

%e 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! +...

%e a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(tan(x)):

%e 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! +...

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

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

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 25 2009