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 A267987 a(n) = Catalan(n)^2*(4n + 4). 1
 4, 8, 48, 400, 3920, 42336, 487872, 5889312, 73616400, 945561760, 12412647104, 165878102208, 2249987591488, 30906422960000, 429157758816000, 6015361252737600, 85011208292365200, 1210159553338375200, 17338543308064440000, 249857534618318088000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Numerator of the modified (4n+4) Wallis-Lambert series with denominator A013709 convergent to 4/Pi. 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: 4/Pi. Q.E.D. LINKS MATHEMATICA Table[CatalanNumber[n]^2 (4 n + 4), {n, 0, 20}] (* Vincenzo Librandi, Jan 24 2016 *) PROG (MAGMA) [Catalan(n)^2*(4*n+4):n in [0..30]]; // Vincenzo Librandi, Jan 24 2016 CROSSREFS Cf. A013709 (denominator). Sequence in context: A054881 A045882 A051681 * A056407 A329942 A056397 Adjacent sequences:  A267984 A267985 A267986 * A267988 A267989 A267990 KEYWORD nonn,easy,frac AUTHOR Ralf Steiner, Jan 23 2016 EXTENSIONS More terms from Vincenzo Librandi, Jan 24 2016 STATUS approved

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Last modified September 22 11:29 EDT 2020. Contains 337289 sequences. (Running on oeis4.)