OFFSET
0,2
FORMULA
a(n) = [x^n/n!] exp(2^n*arcsin(x)) for n >= 0.
EXAMPLE
E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 520*x^3/3! + 66560*x^4/4! + ...
A(x) = 1 + arcsin(2*x) + arcsin(4*x)^2/2! + arcsin(8*x)^3/3! + arcsin(16*x)^4/4! + ... + arcsin(2^n*x)^n/n! + ...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(arcsin(x)):
G(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 20*x^5/5! + 85*x^6/6! + ... + A006228(n)*x^n/n! + ...
PROG
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, asin(2^k*x +x*O(x^n))^k/k!), n)}
(PARI) {a(n)=n!*polcoeff(exp(2^n*asin(x +x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 25 2009
STATUS
approved