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A221020 Reduced denominators 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. 3

%I

%S 1,1,1,2,3,6,5,360,420,56,756,75600,415800,2494800,8424,1223040,

%T 504504000,9081072000,5145940800,111152321280,754247894400,

%U 37712394720000,430747632000,14454741869568,319672175961600,4080179409546240,14011605115200000,1653814216454400000

%N Reduced denominators 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 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 Paul D. Hanna, <a href="/A221020/b221020.txt">Table of n, a(n) for n = 1..150</a>

%F A221019(n)/A221020(n) = A179420(n)/n!.

%e E.g.f. A(x) of A179420 begins:

%e 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 or, equivalently,

%e 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 +...+ A221019(n)/A221020(n)*x^n +...

%e which satisfies: A(A(x)) = x*A'(x) where:

%e A'(x) = 1 + 2*x + 12*x^2/2! + 132*x^3/3! + 2200*x^4/4! +...

%e A(A(x)) = x + 4*x^2/2! + 36*x^3/3! + 528*x^4/4! + 11000*x^5/5! +...

%o (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 n!*polcoeff(subst(A, x, A), n)/(n-2))}

%o {a(n)=denominator(A179420(n)/n!)}

%o for(n=1,25,print1(a(n),","))

%Y Cf. A221019, A179420.

%K nonn,frac

%O 1,4

%A _Paul D. Hanna_, Dec 28 2012

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Last modified January 24 20:52 EST 2022. Contains 350565 sequences. (Running on oeis4.)