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 A235348 Series reversion of x*(1-2*x-5*x^2)/(1-x^2). 1
 1, 2, 12, 82, 636, 5266, 45684, 409706, 3768132, 35346082, 336854844, 3252391170, 31746462732, 312755404818, 3105750620772, 31054695744570, 312404601250644, 3159598296022978, 32108181705850860, 327682918265502002, 3357089384702757276 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of turbulence series A107841 and A235347. LINKS Fung Lam, Table of n, a(n) for n = 1..1000 FORMULA D-finite with recurrence 54*n*(n-1)*a(n) -3*(n-1)*(160*n-237)*a(n-1) +3*(-422*n^2+1721*n-1713)*a(n-2) +2*(-67*n^2+388*n-552)*a(n-3) +(137*n^2-1352*n+3279)*a(n-4) +(7*n-37)*(n-6)*a(n-5) -(n-6)*(n-7)*a(n-6)=0. - R. J. Mathar, Mar 24 2023 MATHEMATICA Rest[CoefficientList[InverseSeries[Series[x*(1-2*x-5*x^2)/(1-x^2), {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Jan 29 2014 *) PROG (Python) # R. J. Mathar, 2023-03-28 class A235348() : def __init__(self) : self.a = [1, 2, 12, 82, 636, 5266] def at(self, n): if n <= len(self.a): return self.a[n-1] else: rhs = -3*(n-1)*(160*n-237)*self.at(n-1) \ +3*(-422*n**2+1721*n-1713)*self.at(n-2) \ +2*(-67*n**2+388*n-552)*self.at(n-3) \ +(137*n**2-1352*n+3279)*self.at(n-4) \ +(7*n-37)*(n-6)*self.at(n-5) -(n-6)*(n-7)*self.at(n-6) rhs //= (-54*n*(n-1)) self.a.append(rhs) return self.a[-1] a235348 = A235348() for n in range(1, 12): print(a235348.at(n)) # a235348. (PARI) Vec( serreverse(x*(1-2*x-5*x^2)/(1-x^2) +O(x^66) ) ) \\ Joerg Arndt, Jan 14 2014 CROSSREFS Sequence in context: A055548 A092850 A199420 * A052864 A355378 A136278 Adjacent sequences: A235345 A235346 A235347 * A235349 A235350 A235351 KEYWORD nonn,easy AUTHOR Fung Lam, Jan 13 2014 STATUS approved

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Last modified December 7 02:20 EST 2023. Contains 367622 sequences. (Running on oeis4.)