A221019 Reduced numerators of A179420(n)/n!, where e.g.f. A(x) = Sum_{n>=0} A179420(n)/n! satisfies: A(A(x)) = x*A'(x) with A(0)=0, A'(0)=1.

1, 1, 2, 11, 55, 419, 1471, 483673, 2756471, 1902667, 139975567, 79889883359, 2616245762827, 97206324428221, 2108611283335, 2036091547932503, 5773060629575464637, 737098816821260577403, 3053528216809788427627, 496374854736310558422419

Offset: 1

Author

Paul D. Hanna, Dec 28 2012

Keywords

• nonn
• frac

Comments

See A179420 for a description of the fascinating properties of the e.g.f. A(x) that satisfies: A(A(x)) = x*A'(x).

Examples

			E.g.f. A(x) of A179420 begins:
A(x) = x + 2*x^2/2! + 12*x^3/3! + 132*x^4/4! + 2200*x^5/5! +...+ A179420(n)/n!*x^n +...
or, equivalently,
A(x) = x + 1/1*x^2 + 2/1*x^3 + 11/2*x^4 + 55/3*x^5 + 419/6*x^6 + 1471/5*x^7 + 483673/360*x^8 + 2756471/420*x^9 + 1902667/56*x^10 +...+ a(n)/A221020(n)*x^n +...
which satisfies: A(A(x)) = x*A'(x) where:
A'(x) = 1 + 2*x + 12*x^2/2! + 132*x^3/3! + 2200*x^4/4! +...
A(A(x)) = x + 4*x^2/2! + 36*x^3/3! + 528*x^4/4! + 11000*x^5/5! +...
		

Links

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

Crossrefs

Cf. A221020, A179420.

Programs

PARI

{A179420(n)=local(A=x+x^2+sum(m=3, n-1, A179420(m)*x^m/m!)+x*O(x^n)); if(n<3, n!*polcoeff(A, n),
n!*polcoeff(subst(A, x, A), n)/(n-2))}
{a(n)=numerator(A179420(n)/n!)}
for(n=1,25,print1(a(n),","))

Formula

a(n)/A221020(n) = A179420(n)/n!.