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 A113180 Expansion of 1/sqrt((1-2*x)^2-8*x^4). 1
 1, 2, 4, 8, 20, 56, 160, 448, 1240, 3440, 9632, 27200, 77216, 219840, 627200, 1793024, 5136480, 14743232, 42390400, 122064640, 351951232, 1015990528, 2936079360, 8493340672, 24591589120, 71262291456, 206666232832, 599778166784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, 1/sqrt((1-a*x)^2-4*b*x^4) expands to Sum_{k=0..floor(n/2)} C(n-2k,k)*C(n-3k,k)*b^k*a^(n-4k). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi) FORMULA a(n) = Sum_{k=0..floor(n/2)} C(n-2k,k)*C(n-3k,k)*2^(n-3k). D-finite with recurrence: n*a(n) = 2*(2*n-1)*a(n-1) - 4*(n-1)*a(n-2) + 8*(n-2)*a(n-4). - Vaclav Kotesovec, Jun 23 2014 a(n) ~ (1+sqrt(1+2*sqrt(2)))^n / (sqrt(6+5*sqrt(2)-sqrt(70+56*sqrt(2))) * sqrt(Pi*n)). - Vaclav Kotesovec, Jun 23 2014 MATHEMATICA CoefficientList[Series[1/Sqrt[(1-2*x)^2-8*x^4], {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 23 2014 *) PROG (PARI) x='x+O('x^50); Vec(1/sqrt((1-2*x)^2 - 8*x^4)) \\ G. C. Greubel, Mar 17 2017 CROSSREFS Cf. A098482, A113179. Sequence in context: A000980 A123611 A082279 * A000116 A302862 A344490 Adjacent sequences: A113177 A113178 A113179 * A113181 A113182 A113183 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 16 2005 STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)