A060629 1/2+Sum_{n >= 1} a(n)*x^(2*n)/(4^n*(2*n)!) = 1/Pi*EllipticK(x).

1, 27, 2250, 385875, 112521150, 49921883550, 31336679474100, 26440323306271875, 28866957423047493750, 39599692192936551926250, 66678681708870074070727500, 135213253391970365203090248750

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

From Vaclav Kotesovec, Nov 14 2023: (Start)

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

a(n) ~ 2^(4*n) * n^(2*n - 1/2) / (sqrt(Pi) * exp(2*n)). (End)

Example

EllipticK(x) = 1/2*Pi + 1/8*Pi*x^2 + 9/128*Pi*x^4 + 25/512*Pi*x^6 + 1225/32768*Pi*x^8 + 3969/131072*Pi*x^10 + O(x^12).

Mathematica

Table[Binomial[2*n, n]*Binomial[2*n - 1, n]*(2*n)!/4^n, {n, 1, 20}] (* Vaclav Kotesovec, Nov 14 2023 *)

Crossrefs

Cf. A038533, A038534.

Sequence in context: A167725 A366181 A272630 * A287228 A086206 A323314

Adjacent sequences: A060626 A060627 A060628 * A060630 A060631 A060632

Keyword

nonn

Author

Vladeta Jovovic, Apr 14 2001

Status

approved