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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

Table of n, a(n) for n=0..18.

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 October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)