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A104629 Expansion of (1-2x-sqrt(1-4x))/(1+2x+sqrt(1-4x))/x^2. 4
1, 2, 6, 18, 57, 186, 622, 2120, 7338, 25724, 91144, 325878, 1174281, 4260282, 15548694, 57048048, 210295326, 778483932, 2892818244, 10786724388, 40347919626, 151355847012, 569274150156, 2146336125648, 8110508473252 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal sums of A039598. a(n)=A000957(n+3).

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(n)=(1+sum{k=0..n+2, C(k)(-2)^k})/(8(-2)^n).

Conjecture: 2*(n+3)*a(n) +(-7*n-9)*a(n-1) +2*(-2*n-3)*a(n-2)=0. - R. J. Mathar, Oct 30 2014

MATHEMATICA

CoefficientList[Series[((1-2x-Sqrt[1-4x])/(1+2x+Sqrt[1-4x]))/x^2, {x, 0, 30}], x] (* Harvey P. Dale, Jul 23 2016 *)

CROSSREFS

Cf. A064310.

Sequence in context: A209797 A064310 A126983 * A000957 A125305 A273203

Adjacent sequences:  A104626 A104627 A104628 * A104630 A104631 A104632

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 17 2005

STATUS

approved

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Last modified March 30 16:23 EDT 2017. Contains 284302 sequences.