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 A192635 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n*A(x^n/(1-x^n))/n ). 1
 1, 1, 2, 5, 16, 57, 234, 1045, 5103, 26791, 150492, 898497, 5676600, 37797128, 264348852, 1936248546, 14814452947, 118126621277, 979597024690, 8432780717866, 75227768490441, 694375113431739, 6622156995890563, 65166502098671053 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare to g.f. G(x) of A000081 (number of rooted trees with n nodes), which satisfies: G(x) = exp( Sum_{n>=1} x^n*G(x^n)/n ). LINKS EXAMPLE G.f.: A(x) =  1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 57*x^5 + 234*x^6 +... The g.f. A(x) satisfies: log(A(x)) = x*A(x/(1-x)) + x^2*A(x^2/(1-x^2))/2 + x^3*A(x^3/(1-x^3))/3 +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, x^m*subst(A, x, x^m/(1-x^m+x*O(x^n)))/m))); polcoeff(A, n)} CROSSREFS Cf. A191412, A192634, A000081. Sequence in context: A188314 A114296 A121689 * A009225 A157612 A184943 Adjacent sequences:  A192632 A192633 A192634 * A192636 A192637 A192638 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 06 2011 STATUS approved

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Last modified October 14 16:29 EDT 2019. Contains 328022 sequences. (Running on oeis4.)