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A294486 a(n) = binomial(2n,n) * (2n+1)^2. 4
1, 18, 150, 980, 5670, 30492, 156156, 772200, 3719430, 17551820, 81477396, 373173528, 1690097500, 7582037400, 33738060600, 149067936720, 654576544710, 2858667619500, 12423860225700, 53760146239800, 231720014946420, 995238809839560, 4260800401533000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..200

Bruno Haible and Thomas Papanikolaou, Fast multiprecision evaluation of series of rational numbers, Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423.

FORMULA

a(n) = A000984(n) * A016754(n).

Sum_{n>=0} 1/a(n) = (8*C - Pi*log(2 + sqrt(3)))/3, where C is Catalan's constant, A006752.

G.f.: (1 + 8*x)/(1 - 4*x)^(5/2). - Ilya Gutkovskiy, Jan 23 2018

MAPLE

seq(binomial(2*n, n) * (2*n + 1)^2, n=0..30); # Muniru A Asiru, Jan 23 2018

MATHEMATICA

Array[Binomial[2 #, #] (2 # + 1)^2 &, 23, 0] (* Michael De Vlieger, Nov 01 2017 *)

PROG

(PARI) a(n) = binomial(2*n, n) * (2*n+1)^2

(GAP) sequence := List([0..10], n-> Binomial(2*n, n) * (2*n + 1)^2); # Muniru A Asiru, Jan 23 2018

(MAGMA) [Binomial(2*n, n)*(2*n+1)^2: n in [0..30]]; // G. C. Greubel, Aug 25 2018

CROSSREFS

Cf. A000984, A006752, A016754.

Sequence in context: A271755 A197214 A027182 * A228994 A235397 A252971

Adjacent sequences:  A294483 A294484 A294485 * A294487 A294488 A294489

KEYWORD

nonn,easy

AUTHOR

Daniel Suteu, Oct 31 2017

STATUS

approved

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Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)