A141363 E.g.f.: A(x) = exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*exp(x*A(x)^6*exp(...))))), an infinite power tower.

1, 1, 9, 175, 5357, 225461, 12112675, 792855043, 61249418585, 5456747990665, 550924441708031, 62176714054787135, 7758184127489208517, 1060631125759075562797, 157674821045525700085499

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

E.g.f.: A(x) = (1/x)*Series_Reversion(x/D(x)) where D(x) is the e.g.f. of A141362.

E.g.f.: A(x) = B(x*A(x)^3) 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)^2) where C(x) = exp(x*C(x)*exp(x*C(x)^2*exp(x*C(x)^3*exp(...)))) is the e.g.f. of A141361 = [1,1,5,55,981,24621,803143,32390247,...].

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

Example

E.g.f.: A(x) = 1 + x + 9*x^2/2! + 175*x^3/3! + 5357*x^4/4! + 225461*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+3)*F)) ; A=F); n!*polcoeff(A, n)}

Crossrefs

Cf. A141360, A141361, A141362; variant: A141359.

Sequence in context: A003280 A201536 A141359 * A157774 A232694 A193443

Adjacent sequences: A141360 A141361 A141362 * A141364 A141365 A141366

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Extensions

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

Status

approved