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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A177406 G.f. satisfies: A(x) = x + A( 27*A(x)^6 )^(1/3). 0
 1, 3, 18, 135, 1134, 10206, 96228, 938304, 9384660, 95746860, 992583072, 10425704562, 110714749236, 1186711306875, 12821975547696, 139501306797120, 1527013735182810, 16805125811826495, 185831030179447380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA Radius of convergence, r, and related values: . r = 0.0832854117848379079627858177662093190328717029025025344504328... . A(r) = 0.166285097718710273401082966562979331796241671228716865630919... . limit a(n)/a(n+1) = r. Series reversion: let R(x) satisfy R(A(x)) = x, then . R(x) = x - A(27x^6)^(1/3), . x/R(x) = x*d/dx[x/R(x)] at x = A(r) where r = radius of convergence. EXAMPLE G.f. A(x) = x + 3*x^2 + 18*x^3 + 135*x^4 + 1134*x^5 + 10206*x^6 +... Related expansions: . A(27*A(x)^6) = 27*x^6 + 486*x^7 + 6561*x^8 + 80190*x^9 +... . A(x)^6 = x^6 + 18*x^7 + 243*x^8 + 2970*x^9 + 34749*x^10 +... . A(27*x^6)^(1/3) = 3*x^2 + 18*x^3 + 135*x^4 + 1134*x^5 + 10206*x^6 +... ... The series reversion is defined by R(x) = x - A(27x^6)^(1/3) where: . R(x) = x - 3*x^2 - 81*x^8 - 10935*x^14 - 2047032*x^20 -... . x/R(x) = 1 + 3*x + 9*x^2 + 27*x^3 + 81*x^4 + 243*x^5 + 729*x^6 + 2268*x^7 +... PROG (PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, 27*(A+x*O(x^n))^6)^(1/3)); polcoeff(A, n)} CROSSREFS Cf. A177408. Sequence in context: A114178 A005159 A151383 * A289430 A247452 A118970 Adjacent sequences:  A177403 A177404 A177405 * A177407 A177408 A177409 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 20 2010 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 June 25 04:15 EDT 2021. Contains 345452 sequences. (Running on oeis4.)