OFFSET
0,2
COMMENTS
Equivalently, coefficient of x^n in the series 1/((2/Pi)E(16x)), where E(x) is the complete elliptic integral of the second kind (defined as in Mathematica, i.e. with x instead of x^2).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..850
FORMULA
Recurrence: a(n+1) = 4*sum(k=0..n, C(k)^2*(2*k+1)*a(n-k) ), where the C(n) are the Catalan numbers (A000108).
Conjecture: a(n) ~ Pi * 2^(4*n-3) / n^2. - Vaclav Kotesovec, Apr 12 2016
MATHEMATICA
CoefficientList[Series[(Pi/2)/EllipticE[16x], {x, 0, 100}], x]
a[0] = 1; Flatten[{1, Table[a[n+1] = 4*Sum[CatalanNumber[k]^2*(2*k + 1)*a[n-k], {k, 0, n}], {n, 0, 20}]}] (* Vaclav Kotesovec, Sep 28 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 30 2011
STATUS
approved