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A284016 a(-1)=-1; a(n) = 2*A000108(n) for n >= 0. 2
-1, 2, 2, 4, 10, 28, 84, 264, 858, 2860, 9724, 33592, 117572, 416024, 1485800, 5348880, 19389690, 70715340, 259289580, 955277400, 3534526380, 13128240840, 48932534040, 182965127280, 686119227300, 2579808294648, 9723892802904, 36734706144304, 139067101832008, 527495903500720, 2004484433302736 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

a(n) = -A002420(n+1).

There exists a set of Ramanujan-Sato series using this sequence.

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

Wikipedia, Ramanujan-Sato series.

FORMULA

a(n) = (2*4^n*Gamma(n+1/2))/(sqrt(Pi)*Gamma(n+2)) for n>= -1. - Ralf Steiner, Apr 02 2017

a(n) = binomial(2*n+2, n+1) / (2*n+1) = 4*binomial(2*n, n) - binomial(2*n+2, n+1) for all n in Z. - Michael Somos, Jan 26 2018

MATHEMATICA

Table[(2*CatalanNumber[n]), {n, -1, 20}]

PROG

(PARI) for(n=-1, 25, print1(round((2*4^n*gamma(n+1/2))/(sqrt(Pi)*gamma(n+2))), ", ")) \\ G. C. Greubel, Apr 11 2017

(PARI) {a(n) = binomial(2*n+2, n+1) / (2*n+1)}; /* Michael Somos, Jan 26 2018 */

(MAGMA) [Binomial(2*n+2, n+1) / (2*n+1): n in [-1..30]]; // Vincenzo Librandi, Jan 27 2018

CROSSREFS

Cf. A002420, A262543, A068875.

Sequence in context: A298898 A078801 A002420 * A112556 A254400 A054100

Adjacent sequences:  A284013 A284014 A284015 * A284017 A284018 A284019

KEYWORD

sign

AUTHOR

Ralf Steiner, Mar 28 2017

STATUS

approved

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Last modified October 23 08:25 EDT 2018. Contains 316521 sequences. (Running on oeis4.)