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 A120603 G.f. satisfies: 16*A(x) = 15 + 27*x + A(x)^7, starting with [1,3,21]. 2
 1, 3, 21, 399, 9135, 233709, 6400947, 183585897, 5443737390, 165536020650, 5133935821014, 161768728483362, 5164132704296202, 166660621950110526, 5428573285691233650, 178234125351736454070, 5892439158797172244515 (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 FORMULA G.f.: A(x) = 1 + Series_Reversion((1+16*x - (1+x)^7)/27). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(7*n,n)/(6*n+1) * (15+27*x)^(6*n+1)/16^(7*n+1). - Paul D. Hanna, Jan 24 2008 a(n) ~ 7^(-13/12 + 2*n) * 9^n * (-245 + 32*2^(2/3)*7^(5/6))^(1/2 - n) / (2^(8/3) * n^(3/2) * sqrt(Pi)). - Vaclav Kotesovec, Nov 28 2017 EXAMPLE A(x) = 1 + 3*x + 21*x^2 + 399*x^3 + 9135*x^4 + 233709*x^5 +... A(x)^7 = 1 + 21*x + 336*x^2 + 6384*x^3 + 146160*x^4 + 3739344*x^5 +... MATHEMATICA CoefficientList[1 + InverseSeries[Series[(1+16*x - (1+x)^7)/27, {x, 0, 20}], x], x] (* Vaclav Kotesovec, Nov 28 2017 *) PROG (PARI) {a(n)=local(A=1+3*x+21*x^2+x*O(x^n)); for(i=0, n, A=A+(-16*A+15+27*x+A^7)/9); polcoeff(A, n)} CROSSREFS Cf. A120588 - A120602, A120604 - A120607. Sequence in context: A108716 A271570 A084620 * A285380 A139224 A032469 Adjacent sequences:  A120600 A120601 A120602 * A120604 A120605 A120606 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 16 2006 STATUS approved

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Last modified March 24 10:22 EDT 2018. Contains 301185 sequences. (Running on oeis4.)