OFFSET
0,2
FORMULA
a(n) = [x^n/n! ] exp(2^n*tan(x)) for n>=0.
EXAMPLE
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! +...
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 25 2009
STATUS
approved