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A126966 Expansion of sqrt(1 - 4*x)/(1 - 2*x). 5
1, 0, -2, -8, -26, -80, -244, -752, -2362, -7584, -24892, -83376, -284324, -984672, -3455144, -12259168, -43908026, -158531392, -576352364, -2107982128, -7750490636, -28629222112, -106190978264, -395347083808, -1476813394916, -5533435084480, -20790762971864, -78316232088032 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A row of an array that is under investigation.

Hankel transform is 2^n*(-1)^binomial(n+1, 2) = A120617(n). - Paul Barry, Feb 08 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = -Sum_{j=0..n} ( 2^j*binomial(2n-2j, n-j)/(2n-2j-1) ). - Emeric Deutsch, Mar 25 2007

Conjecture: n*a(n) + 6*(1-n)*a(n-1) + 4*(3-2*n)*a(n-2) = 0. - R. J. Mathar, Nov 14 2011

a(n) ~ -4^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 29 2013

MAPLE

a:=n->-sum(2^j*binomial(2*n-2*j, n-j)/(2*n-2*j-1), j=0..n): seq(a(n), n=0..27); # Emeric Deutsch, Mar 25 2007

MATHEMATICA

CoefficientList[Series[Sqrt[1 - 4*x]/(1 - 2*x), {x, 0, 50}], x] (* G. C. Greubel, Jan 31 2017 *)

PROG

(PARI) Vec(sqrt(1-4*x)/(1-2*x) + O(x^50)) \\ G. C. Greubel, Jan 31 2017

CROSSREFS

Cf. A126967.

Sequence in context: A103453 A024023 A295137 * A002930 A060410 A128634

Adjacent sequences:  A126963 A126964 A126965 * A126967 A126968 A126969

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Mar 22 2007

STATUS

approved

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Last modified January 22 13:36 EST 2020. Contains 331149 sequences. (Running on oeis4.)