A141357 E.g.f.: A(x) = exp(x*A(x)^2*exp(x^2*A(x)^4*exp(x^3*A(x)^6*exp(x^4*A(x)^8*exp(...))))), an infinite power tower.

1, 1, 5, 55, 945, 21961, 645013, 22948815, 959764865, 46147888945, 2508384505221, 152103283527559, 10179988876061425, 745421842821798585, 59279676127816345685, 5087948349956406532831, 468789320770224531664257

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: A(x) = (1/x)*Series_Reversion(x/B(x)) where B(x) is the e.g.f. of A141356.

E.g.f.: A(x) = x/Series_Reversion(x*C(x)) where C(x) is the e.g.f. of A141358.

E.g.f.: A(x) = B(x*A(x)) 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)^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)^2) 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 + 5*x^2/2! + 55*x^3/3! + 945*x^4/4! + 21961*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))^2)^(n-j+1)*F)); A=F); n!*polcoeff(A, n)}

Crossrefs

Cf. A141356, A141358, A141359; variant: A141361.

Sequence in context: A367164 A008543 A057130 * A357394 A093352 A293013

Adjacent sequences: A141354 A141355 A141356 * A141358 A141359 A141360

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved