A322189 G.f. A(x) satisfies: A(x)^2 + A(x) - 1 = Sum_{n>=0} binomial(3*n,n)^2 * x^n.

1, 3, 72, 2208, 75531, 2748957, 104125542, 4055630148, 161248468944, 6513248563281, 266402605165194, 11007646816287168, 458676184166135532, 19248392999470239126, 812657808793768897362, 34489498873811554580556, 1470421670132406007539195, 62941195430565633995463225, 2703764557673857477236184014, 116513978125127785773539029596

Offset: 0

Author

Paul D. Hanna, Dec 07 2018

Keywords

• nonn

Comments

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

Examples

			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 + ...
		

Crossrefs

Cf. A188662.

Programs

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),", "))