A232607 G.f. A(x) satisfies: (A(x) + x*A'(x)) / (A(x) - x*A(x)^2) = Sum_{n>=0} binomial(2*n,n)^2*x^n.

1, 3, 19, 159, 1546, 16517, 188246, 2248863, 27844369, 354576634, 4618570090, 61289049293, 826064774033, 11281763625102, 155834042142463, 2173801434825011, 30585769379262567, 433633765794690539, 6189637467948022825, 88886796123324352030, 1283443017706197910489, 18623352714450226405962

Offset: 0

Author

Paul D. Hanna, Nov 26 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 3*x + 19*x^2 + 159*x^3 + 1546*x^4 + 16517*x^5 + 188246*x^6 +...
where the g.f. satisfies:
(A(x) + x*A'(x)) / (A(x) - x*A(x)^2) = 1 + 2^2*x + 6^2*x^2 + 20^2*x^3 + 70^2*x^4 + 252^2*x^5 +...+ A000984(n)^2*x^n +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A232606, A000984, A002894.

Programs

PARI

{a(n)=local(CB2=sum(k=0,n,binomial(2*k,k)^2*x^k)+x*O(x^n), A=1+x*O(x^n));
for(i=1,n,A = 1 + intformal( (CB2-1)*A/x - CB2*A^2));polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))

Formula

G.f.: A(x) = (1/x)*Series_Reversion(x/F(x)) where F(x) = A(x/F(x)) is the g.f. of A232606.

Limit n->infinity a(n)^(1/n) = 16. - Vaclav Kotesovec, Jul 05 2014