cp's OEIS Frontend

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.

%I A221019 #16 Jan 10 2013 20:06:15
%S A221019 1,1,2,11,55,419,1471,483673,2756471,1902667,139975567,79889883359,
%T A221019 2616245762827,97206324428221,2108611283335,2036091547932503,
%U A221019 5773060629575464637,737098816821260577403,3053528216809788427627,496374854736310558422419
%N 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.
%C A221019 See A179420 for a description of the fascinating properties of the e.g.f. A(x) that satisfies: A(A(x)) = x*A'(x).
%H A221019 Paul D. Hanna, <a href="/A221019/b221019.txt">Table of n, a(n) for n = 1..150</a>
%F A221019 a(n)/A221020(n) = A179420(n)/n!.
%e A221019 E.g.f. A(x) of A179420 begins:
%e A221019 A(x) = x + 2*x^2/2! + 12*x^3/3! + 132*x^4/4! + 2200*x^5/5! +...+ A179420(n)/n!*x^n +...
%e A221019 or, equivalently,
%e A221019 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 +...
%e A221019 which satisfies: A(A(x)) = x*A'(x) where:
%e A221019 A'(x) = 1 + 2*x + 12*x^2/2! + 132*x^3/3! + 2200*x^4/4! +...
%e A221019 A(A(x)) = x + 4*x^2/2! + 36*x^3/3! + 528*x^4/4! + 11000*x^5/5! +...
%o A221019 (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),
%o A221019 n!*polcoeff(subst(A, x, A), n)/(n-2))}
%o A221019 {a(n)=numerator(A179420(n)/n!)}
%o A221019 for(n=1,25,print1(a(n),","))
%Y A221019 Cf. A221020, A179420.
%K A221019 nonn,frac
%O A221019 1,3
%A A221019 _Paul D. Hanna_, Dec 28 2012