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!)
A189897 E.g.f.: A(x) = exp(x*exp(x*exp(2*x*exp(3*x*exp(...exp(n*x*exp(...))...))))). 0
1, 1, 3, 22, 329, 8636, 355297, 21117286, 1710243761, 180811765432, 24158025584801, 3977274470362634, 790696358461658761, 186695449895152470052, 51635196859642278380513, 16532803795918313120452246 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

FORMULA

E.g.f.: A(x) = exp(x*B(x)) where B(x) is the e.g.f. of A096537.

EXAMPLE

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 329*x^4/4! + 8636*x^5/5! +...

The e.g.f. and related series satisfy:

A(x) = exp(x*B), B = exp(x*C^2), C = exp(x*D^3), D = exp(x*E^4), E = exp(x*F^5), F = exp(x*G^6), ...

where the series begin:

B = 1 + x + 5*x^2/2! + 61*x^3/3! + 1377*x^4/4! + 49721*x^5/5! +...

C = 1 + x + 7*x^2/2! + 118*x^3/3! + 3529*x^4/4! + 162076*x^5/5! +...

D = 1 + x + 9*x^2/2! + 193*x^3/3! + 7169*x^4/4! + 399521*x^5/5! +...

E = 1 + x + 11*x^2/2! + 286*x^3/3! + 12681*x^4/4! + 830876*x^5/5! +...

F = 1 + x + 13*x^2/2! + 397*x^3/3! + 20449*x^4/4! + 1539961*x^5/5! +...

G = 1 + x + 15*x^2/2! + 526*x^3/3! + 30857*x^4/4! + 2625596*x^5/5! +...

Relevant powers of the above series begin:

C^2 = 1 + 2*x + 16*x^2/2! + 278*x^3/3! + 8296*x^4/4! + 375962*x^5/5! +...

D^3 = 1 + 3*x + 33*x^2/2! + 747*x^3/3! + 27921*x^4/4! + 1536723*x^5/5! +...

E^4 = 1 + 4*x + 56*x^2/2! + 1564*x^3/3! + 70416*x^4/4! + 4576724*x^5/5! +...

F^5 = 1 + 5*x + 85*x^2/2! + 2825*x^3/3! + 148945*x^4/4! + 11182925*x^5/5! +...

G^6 = 1 + 6*x + 120*x^2/2! + 4626*x^3/3! + 279672*x^4/4! + 23840046*x^5/5! +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(x*(n-i+1)*A+x*O(x^n))); n!*polcoeff(exp(x*A), n)}

CROSSREFS

Cf. A096537.

Sequence in context: A192036 A229770 A102223 * A306578 A046947 A002485

Adjacent sequences:  A189894 A189895 A189896 * A189898 A189899 A189900

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 01 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 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)