login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

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(...))...))))). 1
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

Vaclav Kotesovec, Table of n, a(n) for n = 0..242

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 November 30 05:12 EST 2021. Contains 349419 sequences. (Running on oeis4.)