The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A143501 G.f. satisfies: A(x) = 1 + x*A(x*A(x)^3). 5
 1, 1, 1, 4, 16, 92, 616, 4729, 40776, 388057, 4028230, 45207583, 544680014, 7004865885, 95694153485, 1382946630490, 21067128029388, 337224872043659, 5656357906530796, 99168643108816180, 1813250965008114981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA G.f. satisfies: G(x) = x/[1 + A(x)*G(x)]^3 = x/A(G(x))^3 where G(x*A(x)^3) = x. EXAMPLE G.f. A(x) = 1 + x + x^2 + 4*x^3 + 16*x^4 + 92*x^5 + 616*x^6 + 4729*x^7 +... A(x)^3 = 1 + 3*x + 6*x^2 + 19*x^3 + 78*x^4 + 411*x^5 + 2617*x^6 +... A(x*A(x)^3) = 1 + x + 4*x^2 + 16*x^3 + 92*x^4 + 616*x^5 + 4729*x^6 +... If G(x*A(x)^3) = x then G(x) = x - 3*x^2 + 12*x^3 - 64*x^4 + 372*x^5 - 2385*x^6 + 15675*x^7 -+... A(G(x)) = 1 + A(x)*G(x) = (x/G(x))^(1/3) where A(x)*G(x) = x - 2*x^2 + 10*x^3 - 51*x^4 + 324*x^5 - 1985*x^6 + 13938*x^7 -... PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, x*A^3)); polcoeff(A, n)} CROSSREFS Cf. A143500. Sequence in context: A009568 A139155 A003762 * A111291 A050913 A096243 Adjacent sequences:  A143498 A143499 A143500 * A143502 A143503 A143504 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 20 2008 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 5 09:45 EST 2021. Contains 349543 sequences. (Running on oeis4.)