A193264 E.g.f. A(x) satisfies: A(A(A(x))) = 2*x*A'(x) - A(x), where A(x) = Sum_{n>=1} a(n)*x^n, with a(1)=1, a(2)=2.

1, 2, 18, 324, 9140, 359460, 18408600, 1174201280, 90423766800, 8215991163000, 865420074120800, 104218992780067440, 14188585798246317120, 2163608674997595229040, 366682177870608886473600, 68611838511981521881152000, 14093827998013078645611495680

Offset: 1

Author

Paul D. Hanna, Jul 20 2011

Keywords

• nonn

Examples

			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! +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A193265, A179420.

Programs

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)))}

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).