OFFSET
0,2
FORMULA
G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2+1)*x^n/n ).
a(n) = (1/n)*Sum_{k=1..n} 2^(k^2+1)*a(n-k), a(0) = 1.
EXAMPLE
G.f.: A(x) = 1 + 4*x + 24*x^2 + 416*x^3 + 34400*x^4 + 13561728*x^5 +...
A(x)^(1/2) = 1 + 2*x + 10*x^2 + 188*x^3 + 16774*x^4 + 6745436*x^5 +...
log(A(x)) = 2^2*x + 2^5*x^2/2 + 2^10*x^3/3 + 2^17*x^4/4 + 2^26*x^5/5 +...
PROG
(PARI) {a(n)=polcoeff(exp( 2*sum(k=1, n, 2^(k^2)*x^k/k)+x*O(x^n)), n)}
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, 2^(k^2+1)*a(n-k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 30 2009
STATUS
approved