OFFSET
0,2
FORMULA
G.f.: 2-AGM(1, 1-8x).
a(n) ~ Pi * 2^(3*n-1) / (n * log(n)^2) * (1 - (2*gamma + 4*log(2))/log(n) + (3*gamma^2 + 12*log(2)*gamma + 12*log(2)^2 - Pi^2/2) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Sep 29 2019
MATHEMATICA
CoefficientList[Series[2 - Pi*(1 - 8*x) / (2*EllipticK[1 - 1/(1 - 8*x)^2]), {x, 0, 25}], x] (* Vaclav Kotesovec, Sep 28 2019 *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff(2-agm(1, 1-8*x+x*O(x^n)), n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 11 2002
STATUS
approved