The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A120595 G.f. satisfies: 13*A(x) = 12 + 27*x + A(x)^4, starting with [1,3,6]. 3
 1, 3, 6, 36, 249, 1932, 16044, 139500, 1253934, 11558316, 108658902, 1037800920, 10041891132, 98230257636, 969814634424, 9651213968784, 96710160474513, 974967422602428, 9881687141571732, 100632995795535588 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n. LINKS Table of n, a(n) for n=0..19. FORMULA G.f.: A(x) = 1 + Series_Reversion((1+13*x - (1+x)^4)/27). G.f.: A(x) = Sum_{n>=0} C(4*n,n)/(3*n+1) * (12 + 27*x)^(3*n+1) / 13^(4*n+1). - Paul D. Hanna, Jan 24 2008 a(n) ~ 2^(3*n - 7/3) * 3^(2*n) / (13^(1/3) * sqrt(Pi) * n^(3/2) * (2^(1/3)*13^(4/3) - 32)^(n - 1/2)). - Vaclav Kotesovec, Nov 27 2017 EXAMPLE A(x) = 1 + 3*x + 6*x^2 + 36*x^3 + 249*x^4 + 1932*x^5 +... A(x)^4 = 1 + 12*x + 78*x^2 + 468*x^3 + 3237*x^4 + 25116*x^5 +... MATHEMATICA CoefficientList[1 + InverseSeries[Series[(1+13*x - (1+x)^4)/27, {x, 0, 20}], x], x] (* Vaclav Kotesovec, Nov 27 2017 *) PROG (PARI) {a(n)=local(A=1+3*x+6*x^2+x*O(x^n)); for(i=0, n, A=A+(-13*A+12+27*x+A^4)/9); polcoeff(A, n)} CROSSREFS Cf. A120588 - A120594, A120596 - A120607; A245043. Sequence in context: A211895 A240986 A372003 * A048642 A264702 A077532 Adjacent sequences: A120592 A120593 A120594 * A120596 A120597 A120598 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 16 2006 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 August 9 20:04 EDT 2024. Contains 375044 sequences. (Running on oeis4.)