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 A229901 G.f. satisfies: A(x) = x*exp( Sum_{n>=1} A(2^n*x^n) / n ). 2
 1, 2, 12, 120, 2208, 75840, 5026048, 654140416, 168815832320, 86777091183104, 89034709122434048, 182521862861195356160, 747975313568170390573056, 6128911186837999697172176896, 100428344706090874604628656668672, 3291036905110044354733349281915109376 (list; graph; refs; listen; history; text; internal format)
 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 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: A048800 A251185 A052738 * A007132 A138534 A062080 Adjacent sequences:  A229898 A229899 A229900 * A229902 A229903 A229904 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 03 2013 STATUS approved

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Last modified September 24 11:38 EDT 2020. Contains 337318 sequences. (Running on oeis4.)