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A322189 G.f. A(x) satisfies: A(x)^2 + A(x) - 1 = Sum_{n>=0} binomial(3*n,n)^2 * x^n. 0
1, 3, 72, 2208, 75531, 2748957, 104125542, 4055630148, 161248468944, 6513248563281, 266402605165194, 11007646816287168, 458676184166135532, 19248392999470239126, 812657808793768897362, 34489498873811554580556, 1470421670132406007539195, 62941195430565633995463225, 2703764557673857477236184014, 116513978125127785773539029596 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Radius of convergence of g.f. A(x) is r = 2^4/3^6 = 16/729.

LINKS

Table of n, a(n) for n=0..19.

EXAMPLE

G.f.: A(x) = 1 + 3*x + 72*x^2 + 2208*x^3 + 75531*x^4 + 2748957*x^5 + 104125542*x^6 + 4055630148*x^7 + 161248468944*x^8 + 6513248563281*x^9 + ...

such that

A(x)^2 + A(x) - 1 = 1 + 9*x + 225*x^2 + 7056*x^3 + 245025*x^4 + 9018009*x^5 + 344622096*x^6 + 13521038400*x^7 + 540917591841*x^8 + 21966328580625*x^9 + ... + binomial(3*n,n)^2 * x^n + ...

PROG

(PARI) {S(n) = sum(m=0, n, binomial(3*m, m)^2 * x^m ) +x*O(x^n)}

{A(n) = (sqrt(4*S(n) + 5) - 1)/2 }

{a(n) = polcoeff( A(n), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A188662.

Sequence in context: A290004 A332188 A071645 * A228712 A300967 A332721

Adjacent sequences:  A322186 A322187 A322188 * A322190 A322191 A322192

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 07 2018

STATUS

approved

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)