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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 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)