OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
FORMULA
G.f.: 1+(K(32x)-1)/4 where K(k)=Elliptic_F(pi/2,k) is the complete Elliptic integral of the first kind;
e.g.f.: BesselI(0, 2*sqrt(2)x)*BesselI(1, 2*sqrt(2)x)/sqrt(2);
a(n) = 2^(n+1)*(binomial(2n,n)/4)^2 - 0^n/8.
Conjecture: n^2*a(n) - (2*n-1)^2*a(n-1) = 0. - R. J. Mathar, Nov 16 2011
MATHEMATICA
Join[{0}, Table[2^(n-1) Binomial[2n-1, n-1]^2, {n, 20}]] (* Harvey P. Dale, Dec 29 2023 *)
PROG
(Magma) [2^(n-1)*Binomial(2*n-1, n-1)^2: n in [0..20]]; // Vincenzo Librandi, Nov 17 2011
(PARI) a(n)=binomial(2*n-1, n-1)^2<<(n-1) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 14 2006
STATUS
approved