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A141531 Inverse binomial transform of A001651. 3
1, 1, 1, -2, 4, -8, 16, -32, 64, -128, 256, -512, 1024, -2048, 4096, -8192, 16384, -32768, 65536, -131072, 262144, -524288, 1048576, -2097152, 4194304, -8388608, 16777216, -33554432, 67108864, -134217728, 268435456, -536870912, 1073741824, -2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (-2).

FORMULA

a(n) = A123344(n+1), n>0.

a(n) = (-2)^n/4 = (-1)^n*A000079(n-2), n>1.

O.g.f.: (1+3x+3x^2)/(1+2x). - R. J. Mathar, Aug 27 2008

a(0)=1, a(1)=1, a(2)=1, a(n) = -2*a(n-1). [Harvey P. Dale, May 04 2012]

G.f.: x+1/Q(0)  where Q(k) = 1 + x*(k+1)/(1 - 1/(1 - (k+1)/Q(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Sep 23 2012

G.f.: 1+x/U(0)  where U(k)=  1 - x*(k+4) + x*(k+3)/U(k+1) ; (continued fraction, 1-step). - Sergei N. Gladkovskii, Oct 11 2012

MATHEMATICA

CoefficientList[Series[(1+3x+3x^2)/(1+2x), {x, 0, 40}], x] (* or *) Join[ {1, 1}, NestList[-2#&, 1, 38]] (* Harvey P. Dale, May 04 2012 *)

Join[{1, 1}, LinearRecurrence[{-2}, {1}, 32]] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Sequence in context: A034008 A123344 * A166444 A084633 A000079 A120617

Adjacent sequences:  A141528 A141529 A141530 * A141532 A141533 A141534

KEYWORD

sign

AUTHOR

Paul Curtz, Aug 12 2008

EXTENSIONS

Edited and extended by R. J. Mathar, Aug 28 2008

STATUS

approved

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Last modified May 24 11:40 EDT 2017. Contains 286975 sequences.