The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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