The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247331 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (3 + A(x)^n)^n. 1
 1, 4, 20, 148, 1492, 18068, 244628, 3582612, 55783252, 913716116, 15633525524, 278068128660, 5124595687636, 97633146977428, 1919960496128660, 38930551809036436, 813367272118600276, 17501331733030883732, 387693438148021391892, 8839040069648710445460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..19. FORMULA G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2)/(1 - 3*x*A(x)^n)^(n+1). EXAMPLE G.f.: A(x) = 1 + 4*x + 20*x^2 + 148*x^3 + 1492*x^4 + 18068*x^5 +... where the g.f. satisfies following series identity: A(x) = 1 + x*(3+A(x)) + x^2*(3+A(x)^2)^2 + x^3*(3+A(x)^3)^3 + x^4*(3+A(x)^4)^4 + x^5*(3+A(x)^5)^5 + x^6*(3+A(x)^6)^6 +... A(x) = 1/(1-3*x) + x*A(x)/(1-3*x*A(x))^2 + x^2*A(x)^4/(1-3*x*A(x)^2)^3 + x^3*A(x)^9/(1-3*x*A(x)^3)^4 + x^4*A(x)^16/(1-3*x*A(x)^4)^5 + x^5*A(x)^25/(1-3*x*A(x)^5)^6 + x^6*A(x)^36/(1-3*x*A(x)^6)^7 +... PROG (PARI) {a(n, t=3)=local(A=1+x); for(i=1, n, A=sum(k=0, n, A^(k^2)*x^k/(1 - t*A^k*x +x*O(x^n))^(k+1) )); polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) (PARI) {a(n, t=3)=local(A=1+x); for(i=1, n, A=sum(k=0, n, x^k * (t + A^k +x*O(x^n))^k)); polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A247330, A203000. Sequence in context: A117887 A082988 A001171 * A167018 A094070 A335627 Adjacent sequences: A247328 A247329 A247330 * A247332 A247333 A247334 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 14 2014 STATUS approved

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

Last modified June 18 23:53 EDT 2024. Contains 373490 sequences. (Running on oeis4.)