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 A192634 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n*A(x^n + x^(2*n))/n ). 1
 1, 1, 2, 5, 15, 50, 191, 789, 3566, 17306, 89871, 496250, 2901931, 17901455, 116129282, 789973067, 5620945352, 41739598787, 322802306649, 2595133213658, 21650633864406, 187146890460633, 1673639663735620, 15464023782414504, 147441877065741283 (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 + 15*x^4 + 50*x^5 + 191*x^6 +... The g.f. satisfies: log(A(x)) = x*A(x+x^2) + x^2*A(x^2+x^4)/2 + x^3*A(x^3+x^6)/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+x^(2*m)+x*O(x^n))/m))); polcoeff(A, n)} CROSSREFS Cf. A192635, A000081. Sequence in context: A245311 A148367 A306836 * A304386 A140639 A149953 Adjacent sequences:  A192631 A192632 A192633 * A192635 A192636 A192637 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 06 2011 STATUS approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)