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A166229 Expansion of (1-2x-sqrt(1-8x+8x^2))/(2x). 4
1, 2, 8, 36, 176, 912, 4928, 27472, 156864, 912832, 5394176, 32282240, 195264000, 1191825920, 7331457024, 45406194944, 282896763904, 1771868302336, 11150040870912, 70461597988864, 446971590516736, 2845144452292608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A166228. Hankel transform is A166231.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

FORMULA

a(n)=0^n+sum{k=0..n, C(n-1,k-1)*A006318(k)}. [From Paul Barry, Nov 04 2009]

G.f.: 1/(1-2x/(1-x-x/(1-2x/(1-x-x/(1-2x/(1-x-x/(1-... (continued fraction). [From Paul Barry, Dec 10 2009]

Recurrence: (n+1)*a(n) = 4*(2*n-1)*a(n-1) - 8*(n-2)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ sqrt(1+sqrt(2))*(4+2*sqrt(2))^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012

MATHEMATICA

CoefficientList[Series[(1-2*x-Sqrt[1-8*x+8*x^2])/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

CROSSREFS

Sequence in context: A186338 A190862 A110837 * A109318 A113327 A227791

Adjacent sequences:  A166226 A166227 A166228 * A166230 A166231 A166232

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 09 2009

STATUS

approved

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Last modified October 18 03:46 EDT 2018. Contains 316304 sequences. (Running on oeis4.)