A229901 G.f. satisfies: A(x) = x*exp( Sum_{n>=1} A(2^n*x^n) / n ).

1, 2, 12, 120, 2208, 75840, 5026048, 654140416, 168815832320, 86777091183104, 89034709122434048, 182521862861195356160, 747975313568170390573056, 6128911186837999697172176896, 100428344706090874604628656668672, 3291036905110044354733349281915109376

Offset

1,2

Comments

Compare to: G(x) = x*exp( Sum_{n>=1} G(x^n)/n ), which is the g.f. of A000081, the number of rooted trees with n nodes.

Links

Table of n, a(n) for n=1..16.

Formula

Limit a(n) / 2^(n*(n-1)/2) = 2.4760521181770989525583758338042055853633514575492...

Example

G.f.: A(x) = x + 2*x^2 + 12*x^3 + 120*x^4 + 2208*x^5 + 75840*x^6 + 5026048*x^7 + ...
where
A(x) = x*exp(A(2*x) + A(4*x^2)/2 + A(8*x^3)/3 + A(16*x^4)/4 + A(32*x^5)/5 + A(64*x^6)/6 + A(128*x^7)/7 + A(256*x^8)/8 + A(512*x^9)/9 + A(1024*x^10)/10 + ...).

Prog

(PARI) {a(n)=local(A=x); for(i=1, n, A=x*exp(sum(k=1, n, subst(A, x, 2^k*x^k +x*O(x^n))/k))); polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A000081, A229900, A229807.

Sequence in context: A251185 A052738 A373433 * A007132 A138534 A062080

Adjacent sequences: A229898 A229899 A229900 * A229902 A229903 A229904

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2013

Status

approved