OFFSET
1,4
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).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..150
EXAMPLE
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 +...+ A221019(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! +...
PROG
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Paul D. Hanna, Dec 28 2012
STATUS
approved