login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A186632 E.g.f. satisfies: A(A(A(x))) = d/dx A(x)^2/2 with A(0)=0, A'(0)=1. 0
1, 2, 24, 588, 22560, 1201320, 82875744, 7085373456, 727827579648, 87810122446560, 12227912455651200, 1938610503725962176, 346053263639068417536, 68919212804888587849344 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..14.

FORMULA

E.g.f. satisfies: A(A(A(x))) = A'(x)*A(x).

E.g.f. satisfies: A(A(A(A(x)))) = A'(A(x))*A(A(x)) = A( A'(x)*A(x) ).

E.g.f. satisfies: A(A(A(A(A(x))))) = A'(A(A(x)))*A'(x)*A(x).

n(n-1) divides a(n) for n>=2.

EXAMPLE

E.g.f: A(x) = x + 2*x^2/2! + 24*x^3/3! + 588*x^4/4! + 22560*x^5/5! +...

A(x)^2/2 = x^2/2! + 6*x^3/3! + 108*x^4/4! + 3420*x^5/5! + 158760*x^6/6! +...

Iterations of the e.g.f. begin:

A(A(x)) = x + 4*x^2/2! + 60*x^3/3! + 1680*x^4/4! + 70920*x^5/5! +...

A(A(A(x))) = x + 6*x^2/2! + 108*x^3/3! + 3420*x^4/4! + 158760*x^5/5! +...

A(A(A(A(x)))) = x + 8*x^2/2! + 168*x^3/3! + 5952*x^4/4! + 302640*x^5/5! +...

A(A(A(A(A(x))))) = x + 10*x^2/2! + 240*x^3/3! + 9420*x^4/4! + 522000*x^5/5! +...

Related expansions:

A'(A(x)) = 1 + 2*x + 28*x^2/2! + 780*x^3/3! + 33384*x^4/4! + 1956120*x^5/5! +...

A'(A(A(x))) = 1 + 2*x + 32*x^2/2! + 996*x^3/3! + 46944*x^4/4! + 2998680*x^5/5! +...

PROG

(PARI) {a(n)=local(A=x+x^2+sum(m=3, n-1, a(m)*x^m/m!)+x*O(x^n)); if(n<3, n!*polcoeff(A, n), n!*polcoeff(subst(A, x, subst(A, x, A))-deriv(A^2/2), n)/(n-2))}

CROSSREFS

Cf. A179420.

Sequence in context: A280794 A090316 A128578 * A089835 A210909 A009251

Adjacent sequences:  A186629 A186630 A186631 * A186633 A186634 A186635

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 24 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)