A141358 E.g.f.: A(x) = exp(x*A(x)^3*exp(x^2*A(x)^6*exp(x^3*A(x)^9*exp(x^4*A(x)^12*exp(...))))), an infinite power tower.

1, 1, 7, 106, 2509, 80956, 3313579, 164514904, 9608077945, 645470256592, 49038954301711, 4157529546929056, 389125813949115973, 39853422352958799040, 4433527105413108692851, 532370587431255626482816

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 A141357.

E.g.f.: A(x) = x/Series_Reversion(x*D(x)) where D(x) is the e.g.f. of A141359.

E.g.f.: A(x) = B(x*A(x)^2) where B(x) = exp(x*B(x)*exp(x^2*B(x)^2*exp(x^3*B(x)^3*exp(...)))) is the e.g.f. of A141356 = [1,1,3,22,245,3516,63727,1405384,...].

E.g.f.: A(x) = C(x*A(x)) where C(x) = exp(x*C(x)^2*exp(x^2*C(x)^4*exp(x^3*C(x)^6*exp(...)))) is the e.g.f. of A141357 = [1,1,5,55,945,21961,645013,22948815,...].

E.g.f.: A(x) = D(x/A(x)) where D(x) = exp(x*D(x)^4*exp(x^2*D(x)^8*exp(x^3*D(x)^12*exp(...)))) is the e.g.f. of A141359 = [1,1,9,175,5321,221001,11659345,746678311,...].

Example

E.g.f.: A(x) = 1 + x + 7*x^2/2! + 106*x^3/3! + 2509*x^4/4! + 80956*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))^3)^(n-j+1)*F)); A=F); n!*polcoeff(A, n)}

Crossrefs

Cf. A141356, A141357, A141359; variant: A141362.

Sequence in context: A203971 A145167 A367166 * A141362 A213863 A231899

Adjacent sequences: A141355 A141356 A141357 * A141359 A141360 A141361

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved