A141356 E.g.f.: A(x) = exp(x*A(x)*exp(x^2*A(x)^2*exp(x^3*A(x)^3*exp(x^4*A(x)^4*exp(...))))), an infinite power tower.

1, 1, 3, 22, 245, 3516, 63727, 1405384, 36336393, 1077150160, 36056947931, 1345603208544, 55390366280317, 2493292939893952, 121840258072947975, 6423982984221479296, 363498003830522845073, 21972216426996693494016

Offset

0,3

Links

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

Formula

E.g.f.: A(x) = x/Series_Reversion(x*B(x)) where B(x) is the e.g.f. of A141357.

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

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

E.g.f.: A(x) = D(x/A(x)^3) 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 + 3*x^2/2! + 22*x^3/3! + 245*x^4/4! + 3516*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+1)*F)); A=F); n!*polcoeff(A, n)}

Crossrefs

Cf. A141357, A141358, A141359; variant: A141360.

Sequence in context: A141006 A367835 A042703 * A335309 A162633 A052677

Adjacent sequences: A141353 A141354 A141355 * A141357 A141358 A141359

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved