A141359 E.g.f.: A(x) = exp(x*A(x)^4*exp(x^2*A(x)^8*exp(x^3*A(x)^12*exp(x^4*A(x)^16*exp(...))))), an infinite power tower.

1, 1, 9, 175, 5321, 221001, 11659345, 746678311, 56273809905, 4879911980017, 478663176441401, 52401160551586815, 6333742154439370489, 837795219321504405625, 120379591345300309348929

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 A141358.

E.g.f.: A(x) = B(x*A(x)^3) 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)^2) 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)^3*exp(x^2*D(x)^6*exp(x^3*D(x)^9*exp(...)))) is the e.g.f. of A141358 = [1,1,7,106,2509,80956,3313579,164514904,...].

Example

E.g.f.: A(x) = 1 + x + 9*x^2/2! + 175*x^3/3! + 5321*x^4/4! + 221001*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))^4)^(n-j+1)*F)); A=F); n!*polcoeff(A, n)}

Crossrefs

Cf. A141356, A141357, A141358; variant: A141363.

Sequence in context: A027956 A003280 A201536 * A141363 A157774 A232694

Adjacent sequences: A141356 A141357 A141358 * A141360 A141361 A141362

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved