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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

Table of n, a(n) for n=0..19.

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: A076687 A045882 A051681 * A056407 A056397 A189314

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 March 25 11:52 EDT 2017. Contains 284076 sequences.