OFFSET
0,1
COMMENTS
Numerator of the modified (4n+3) Wallis-Lambert-series-1 with denominator A013709 convergent to 1. Proof: Both the Wallis-Lambert-series-1=4/Pi-1 and the elliptic Euler-series=1-2/Pi are absolutely convergent series. Thus any linear combination of the terms of these series will be also absolutely convergent to the value of the linear combination of these series - in this case to 1. Q.E.D.
LINKS
Ralf Steiner, Notiz zur modifizierten Wallis-Lambert-Reihe (in German).
FORMULA
a(n) = Catalan(n)^2*(4n + 3).
MATHEMATICA
Table[CatalanNumber[n]^2 (4 n + 3), {n, 0, 19}] (* Michael De Vlieger, Jan 24 2016 *)
PROG
(Magma) [Catalan(n)^2*(4*n+3):n in [0..20]]; // Vincenzo Librandi, Jan 25 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ralf Steiner, Jan 21 2016
STATUS
approved