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 A192206 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^n/(1 - x^n*A(x)^n). 3
 1, 1, 3, 9, 32, 118, 460, 1844, 7587, 31804, 135433, 584092, 2546250, 11201310, 49663816, 221701658, 995621590, 4494862920, 20388491423, 92872814115, 424665159560, 1948516758192, 8968647197842, 41399782218408, 191608577837136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA G.f. satisfies: A(x) = 1 + Sum_{n>=1} tau(n)*x^n*A(x)^n, where tau(n) = the number of divisors of n (A000005). G.f. satisfies: G(x) = A(x/G(x)) where G(x) = 1 + Sum_{n>=1} x^n/(1 - x^n) is a g.f. for A000005. EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 32*x^4 + 118*x^5 + 460*x^6 +... which satisfies: A(x) = 1 + x*A(x)/(1-x*A(x)) + x^2*A(x)^2/(1-x^2*A(x)^2) + x^3*A(x)^3/(1-x^3*A(x)^3) +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*A^m/(1-x^m*A^m+x*O(x^n)))); polcoeff(A, n)} (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, sigma(m, 0)*x^m*A^m+x*O(x^n))); polcoeff(A, n)} CROSSREFS Cf. A000005. Sequence in context: A148986 A052872 A122452 * A091841 A063020 A104184 Adjacent sequences:  A192203 A192204 A192205 * A192207 A192208 A192209 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 25 2011 STATUS approved

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Last modified April 18 07:54 EDT 2021. Contains 343084 sequences. (Running on oeis4.)