A180720 G.f: A(x) = exp(Sum_{n>=1} A(L(n)*x)^n*x^n/n) = exp(Sum_{n>=1} L(n)*x^n/n) where L(n) = A180721(n).

1, 1, 2, 7, 53, 1305, 177559, 247880897, 9252468642944, 39211218810149955871, 155393322265527728403643204013, 12102963126133848174768954972642433817636369

Offset

0,3

Comments

Terms seem to be doubly-exponential: log(a(n+1))/log(a(n)) ~ c where c = 1.44...

Links

Table of n, a(n) for n=0..11.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 53*x^4 + 1305*x^5 + 177559*x^6 +...
The logarithm of g.f. A(x) begins:
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 183*x^4/4 + 6236*x^5/5 + 1057176*x^6/6 + 1733913028*x^7/7 + 74017764628367*x^8/8 +...+ A180721(n)*x^n/n +...
which also equals the series:
log(A(x)) = A(x)*x + A(3*x)^2*x^2/2 + A(16*x)^3*x^3/3 + A(183*x)^4*x^4/4 + A(6236*x)^5*x^5/5 + A(1057176*x)^6*x^6/6 + A(1733913028*x)^7*x^7/7 +...+ A(A180721(n)*x)^n*x^n/n + ...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n), L); for(i=1, n, L=Vec(deriv(log(A))); A=exp(sum(m=1, #L, subst(A, x, L[m]*x)^m*x^m/m)+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Cf. A180721.

Sequence in context: A104084 A053465 A193191 * A168558 A024027 A079410

Adjacent sequences: A180717 A180718 A180719 * A180721 A180722 A180723

Keyword

nonn

Author

Paul D. Hanna, Sep 19 2010

Status

approved