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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, 3578416722896540323224657, 446526125468639494991613297 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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) = my(A=1+x + x*O(x^n), F); for(i=0, n+1, for(j=0, n, F = exp(x*(A + x*O(x^n))^(n-j+1) * F)); A=F); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Cf. A141360, A141362, A141363; variant: A141357.
Sequence in context: A172493 A155807 A135861 * A203013 A266481 A371316
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 June 24 18:26 EDT 2024. Contains 373688 sequences. (Running on oeis4.)