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 A214668 G.f. satisfies: A(x) = 1 + 9*x*A(x)^(4/3). 1
 1, 9, 108, 1458, 21060, 318087, 4960116, 79227720, 1289516436, 21308126895, 356506456680, 6027199821864, 102804351279084, 1766931074710515, 30570993847594800, 532022685332573016, 9306598678048938420, 163549467160708850910, 2886019647490699098588 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Radius of convergence of g.f. A(x) is r = 1/(3*4^(4/3)) where A(r) = 4. Self-convolution cube of A078532. LINKS FORMULA a(n) = 9^n * binomial(4*n/3, n) / (n/3 + 1). EXAMPLE G.f.: A(x) = 1 + 9*x + 108*x^2 + 1458*x^3 + 21060*x^4 + 318087*x^5 +... where A(x) = 1 + 9*x*A(x)^(4/3). Radius of convergence: r = 1/(3*4^(4/3)) = 0.052496710... Related expansions: A(x)^(4/3) = 1 + 12*x + 162*x^2 + 2340*x^3 + 35343*x^4 + 551124*x^5 +...+ a(n+1)/9*x^n +... A(x)^(1/3) = 1 + 3*x + 27*x^2 + 315*x^3 + 4158*x^4 + 59049*x^5 + 880308*x^6 + 13586859*x^7 + 215233605*x^8 +...+ A078532(n)*x^n +... PROG (PARI) {a(n)=9^n*binomial(4*n/3, n)/(n/3+1)} (PARI) {a(n)=local(A=1+x); for(i=1, n, A =1+9*x*(A+x*O(x^n))^(4/3)); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A078532, A214377, A214553. Sequence in context: A104224 A099676 A268839 * A234467 A288550 A166907 Adjacent sequences:  A214665 A214666 A214667 * A214669 A214670 A214671 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 24 2012 STATUS approved

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Last modified May 6 21:35 EDT 2021. Contains 343597 sequences. (Running on oeis4.)