A179471 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(2^n*x^n)*x^n/n ).

1, 1, 3, 15, 139, 2387, 79115, 5148411, 664332843, 170744863371, 87593505706987, 89783692196468907, 183966962290186844267, 753712824966410639243755, 6175169543791440589003293035, 101180154484297968338398947674219

Offset

0,3

Comments

Compare to g.f. of A157675: G(x) = exp( Sum_{n>=1} G(2^n*x)^n*x^n/n ).

Links

Table of n, a(n) for n=0..15.

Formula

Limit a(n) / 2^(n*(n-1)/2) = 2.494435637496531683539561928813688982084486211124...

Example

G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 139*x^4 + 2387*x^5 +...
log(A(x)) = A(2x) + A(4x^2)*x^2/2 + A(8x^3)*x^3/3 + A(16x^4)*x^4/4 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, 2^m*x^m+x*O(x^n))*x^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A157675.

Sequence in context: A005816 A179470 A270524 * A203417 A086228 A288456

Adjacent sequences: A179468 A179469 A179470 * A179472 A179473 A179474

Keyword

nonn

Author

Paul D. Hanna, Jul 15 2010

Status

approved