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.

1, 1, 5, 55, 981, 24621, 803143, 32390247, 1560845289, 87688371385, 5637912173451, 408922311037659, 33077570245035517, 2956347175261764597, 289716070585295689455, 30931475430329804121871, 3578416722896540323224657, 446526125468639494991613297

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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

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