OFFSET
1,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..150
FORMULA
E.g.f. A(x) satisfies: A(A(A(x))) = Sum_{n>=1} (2*n-1)*a(n)*x^n.
a(n) = n*A193265(n-1).
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! + 18*x^3/3! + 324*x^4/4! + 9140*x^5/5! + 359460*x^6/6! +...+ a(n)*x^n/n! +...
where
A(A(A(x))) = x + 6*x^2/2! + 90*x^3/3! + 2268*x^4/4! + 82260*x^5/5! + 3954060*x^6/6! +...+ (2*n-1)*a(n)*x^n/n! +...
which equals:
2*x*A'(x) - A(x) = x + 3*2*x^2/2! + 5*18*x^3/3! + 7*324*x^4/4! + 9*9140*x^5/5! +...
PROG
(PARI) {a(n)=local(A=x); if(n<1, 0, if(n<=2, n, A=x+sum(m=2, n-1, a(m)*x^m/m!)+x*O(x^n);
n!*polcoeff(subst(A, x, subst(A, x, A))-2*x*A', n)/(2*n-4)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 20 2011
STATUS
approved