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A245113 G.f. satisfies: A(x)^2 = 1 + 4*x*A(x)^6. 2
1, 2, 22, 340, 6118, 120060, 2492028, 53798888, 1195684230, 27175425004, 628705751828, 14756641134872, 350529497005532, 8410852483002200, 203561027031883320, 4963404936414528720, 121810229481173225670, 3006555636255509030220, 74585744314812449403300, 1858695101618327423328312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Radius of convergence of g.f. A(x) is r = 1/27 where A(r) = sqrt(3/2).

LINKS

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

FORMULA

a(n) = 4^n * binomial((6*n - 1)/2, n) / (4*n + 1).

G.f. satisfies: A(x) = sqrt(1 + 4*x^2*A(x)^10) + 2*x*A(x)^5.

G.f.: A(x) = sqrt(D(4*x)), where D(x) is the g.f. of A001764. - Werner Schulte, Aug 10 2015

EXAMPLE

G.f.: A(x) = 1 + 2*x + 22*x^2 + 340*x^3 + 6118*x^4 + 120060*x^5 + ...

where A(x)^2 = 1 + 4*x*A(x)^6:

A(x)^2 = 1 + 4*x + 48*x^2 + 768*x^3 + 14080*x^4 + 279552*x^5 + ...

A(x)^6 = 1 + 12*x + 192*x^2 + 3520*x^3 + 69888*x^4 + 1462272*x^5 + ...

Related series:

A(x)^5 = 1 + 10*x + 150*x^2 + 2660*x^3 + 51750*x^4 + 1068012*x^5 + ...

A(x)^10 = 1 + 20*x + 400*x^2 + 8320*x^3 + 179200*x^4 + 3969024*x^5 + ...

where A(x) = sqrt(1 + 4*x^2*A(x)^10) + 2*x*A(x)^5.

MAPLE

A245113:=n->4^n*binomial((6*n-1)/2, n)/(4*n+1): seq(A245113(n), n=0..30); # Wesley Ivan Hurt, Aug 11 2015

MATHEMATICA

Table[4^n*Binomial[(6 n - 1)/2, n]/(4 n + 1), {n, 0, 20}] (* Wesley Ivan Hurt, Aug 11 2015 *)

PROG

(PARI) /* From A(x)^2 = 1 + 4*x*A(x)^6 : */

{a(n) = local(A=1+x); for(i=1, n, A=sqrt(1 + 4*x*A^6 +x*O(x^n))); polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

(PARI) {a(n) = 4^n * binomial((6*n - 1)/2, n) / (4*n + 1)}

for(n=0, 20, print1(a(n), ", "))

(PARI) /* From A(x) = sqrt(1 + 4*x^2*A(x)^10) + 2*x*A(x)^5 : */

{a(n) = local(A=1+x); for(i=1, n, A = sqrt(1 + 4*x^2*A^10 +x*O(x^n)) + 2*x*A^5); polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A245112, A245114.

Sequence in context: A266888 A155674 A279619 * A078232 A151615 A111985

Adjacent sequences:  A245110 A245111 A245112 * A245114 A245115 A245116

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Jul 31 2014

STATUS

approved

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Last modified December 5 15:06 EST 2021. Contains 349557 sequences. (Running on oeis4.)