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 A113179 Expansion of 1/sqrt((1-2x)^2-8x^3). 2
 1, 2, 4, 12, 40, 128, 408, 1328, 4384, 14560, 48576, 162816, 547936, 1850048, 6263680, 21257856, 72298240, 246345728, 840775424, 2873802240, 9835840512, 33704557568, 115622041600, 397032488960, 1364610270720, 4694145256448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, 1/sqrt((1-a*x)^2-4*b*x^3) expands to sum{k=0..floor(n/2), C(n-k,k)C(n-2k,k)b^k*a^(n-3k)}. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..1837 Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5. FORMULA a(n)=sum{k=0..floor(n/2), C(n-k, k)C(n-2k, k)2^(n-2k)}. D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. [Belbachir] MATHEMATICA CoefficientList[Series[1/Sqrt[(1-2x)^2-8x^3], {x, 0, 30}], x] (* Harvey P. Dale, Dec 23 2017 *) CROSSREFS Cf. A098479. Sequence in context: A170808 A099214 A126946 * A214761 A327845 A056236 Adjacent sequences: A113176 A113177 A113178 * A113180 A113181 A113182 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 16 2005 STATUS approved

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Last modified September 26 02:15 EDT 2023. Contains 365649 sequences. (Running on oeis4.)