A141362 E.g.f.: A(x) = exp(x*A(x)^2*exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*exp(...))))), an infinite power tower.

1, 1, 7, 106, 2545, 84516, 3599869, 187549426, 11569862497, 825476139784, 66913201813141, 6077199111018366, 611543851953714673, 67563014389049920924, 8132697862579447135021, 1059750845948899631017906

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f.: A(x) = (1/x)*Series_Reversion(x/C(x)) where C(x) is the e.g.f. of A141361.

E.g.f.: A(x) = x/Series_Reversion(x*D(x)) where D(x) is the e.g.f. of A141363.

E.g.f.: A(x) = B(x*A(x)^2) 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)*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)^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 + 7*x^2/2! + 106*x^3/3! + 2545*x^4/4! +
84516*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+2)*F)) ; A=F); n!*polcoeff(A, n)}

Crossrefs

Cf. A141360, A141361, A141363; variant: A141358.

Sequence in context: A145167 A367166 A141358 * A213863 A231899 A188407

Adjacent sequences: A141359 A141360 A141361 * A141363 A141364 A141365

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved