OFFSET
1,2
FORMULA
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! + 12*x^3/3! + 128*x^4/4! + 2016*x^5/5! +...
Related expansions:
A'(x) = 1 + 2*x + 12*x^2/2! + 128*x^3/3! + 2016*x^4/4! + 42656*x^5/5! +...
A(A(x)) = log(A'(x))/2 = x + 4*x^2/2! + 36*x^3/3! + 520*x^4/4! + 10512*x^5/5! + 276064*x^6/6! + 8987712*x^7/7! + 351278080*x^8/8! +...
The exponential of e.g.f. A(x) equals the e.g.f. of A233336:
exp(A(x)) = 1 + x + 3*x^2/2! + 19*x^3/3! + 201*x^4/4! + 3097*x^5/5! + 63963*x^6/6! + 1677883*x^7/7! +...+ A233336(n)*x^n/n! +...
PROG
(PARI) {a(n)=local(A=x+x^2); for(i=0, n, A=intformal(exp(2*subst(A, x, A+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 03 2015
STATUS
approved