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A141361 E.g.f.: A(x) = exp(x*A(x)*exp(x*A(x)^2*exp(x*A(x)^3*exp(x*A(x)^4*exp(...))))), an infinite power tower. 4
1, 1, 5, 55, 981, 24621, 803143, 32390247, 1560845289, 87688371385, 5637912173451, 408922311037659, 33077570245035517, 2956347175261764597, 289716070585295689455, 30931475430329804121871 (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) = (1/x)*Series_Reversion(x/B(x)) where B(x) is the e.g.f. of A141360.

E.g.f.: A(x) = x/Series_Reversion(x*C(x)) where C(x) is the e.g.f. of A141362.

E.g.f.: A(x) = B(x*A(x)) where B(x) = exp(x*exp(x*B(x)*exp(x*B(x)^2*exp(x*B(x)^3*exp(...))))) is the e.g.f. of A141360 = [1,1,3,22,281,5276,132577,4209766,...].

E.g.f.: A(x) = C(x/A(x)) where C(x) = exp(x*C(x)^2*exp(x*C(x)^3*exp(x*C(x)^4*exp(...)))) is the e.g.f. of A141362 = [1,1,7,106,2545,84516,3599869,187549426,...].

E.g.f.: A(x) = D(x/A(x)^2) where D(x) = exp(x*D(x)^3*exp(x*D(x)^4*exp(x*D(x)^5*exp(...)))) is the e.g.f. of A141363 = [1,1,9,175,5357,225461,12112675,792855043,...].

EXAMPLE

E.g.f.: A(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 981*x^4/4! +

24621*x^5/5! +...

PROG

(PARI) {a(n)=local(A=1+x, F); for(i=0, n, for(j=0, n, F=exp(x*(A+x*O(x^n))^(n-j+1)*F)) ; A=F); n!*polcoeff(A, n)}

CROSSREFS

Cf. A141360, A141362, A141363; variant: A141357.

Sequence in context: A172493 A155807 A135861 * A203013 A266481 A006150

Adjacent sequences:  A141358 A141359 A141360 * A141362 A141363 A141364

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 28 2008

EXTENSIONS

Typo in data corrected by D. S. McNeil, Aug 17 2010

STATUS

approved

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Last modified March 29 06:34 EDT 2017. Contains 284250 sequences.