This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)