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 A217363 Series reversion of x - 3*x^3. 3
 1, 3, 27, 324, 4455, 66339, 1041012, 16953624, 283848543, 4855304025, 84482290035, 1490628232080, 26607713942628, 479621100042756, 8718235759397880, 159628084420459248, 2941328850997439439, 54501093415540789605, 1014898739548854163185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Regular zeros in the reverted sequence have been left out: If y = x - 3*x^3, then x = y + 3*y^3 + 27*y^5 + 324*y^7 + 4455*y^9 + 66339*y^11 + ... REFERENCES Number of lattice paths that do not go below the x-axis from (0,0) to (3n,0) using steps D(1,-1) and three types of U(1,2). - David Scambler, Jun 22 2013 LINKS Robert Israel, Table of n, a(n) for n = 1..769 R. J. Mathar, Series Expansion of Generalized Fresnel Integrals, arXiv:1211.3963 [math.CA], 2012, App. A. FORMULA (2*n-1)*(2*n-2)*a(n) - 9*(3*n-4)*(3*n-5)*a(n-1) = 0. a(n) = 3^(n-1)*A001764(n-1). From Benedict W. J. Irwin, Jul 12 2016: (Start) G.f.: (2/3)*sqrt(x)*sin(asin(9*sqrt(x)/2)/3). E.g.f.: x*2F2(1/3,2/3;3/2,2;81*x/4). (End) a(n) ~ 3^(4*n - 7/2)*4^(-n)*n^(-3/2)/sqrt(Pi). - Ilya Gutkovskiy, Jul 12 2016 MAPLE f:= k -> (3*k-3)!*3^(k-1)/(k-1)!/(2*k-1)!: map(f, [\$1..30]); # Robert Israel, May 07 2017 MATHEMATICA CoefficientList[Series[2/3 Sqrt[z] Sin[ArcSin[(9 Sqrt[z])/2]/3], {z, 0, 20}], z](* Benedict W. J. Irwin, Jul 12 2016 *) CROSSREFS Cf. A005159 (revert x-3*x^2), A153231 (revert x-2*x^3). Sequence in context: A291315 A078532 A264684 * A234462 A153853 A067000 Adjacent sequences:  A217360 A217361 A217362 * A217364 A217365 A217366 KEYWORD nonn,easy AUTHOR R. J. Mathar, Oct 01 2012 STATUS approved

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Last modified December 8 02:32 EST 2021. Contains 349590 sequences. (Running on oeis4.)