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A235348 Series reversion of x*(1-2*x-5*x^2)/(1-x^2).

%I A235348 #22 Mar 28 2023 12:18:24
%S A235348 1,2,12,82,636,5266,45684,409706,3768132,35346082,336854844,
%T A235348 3252391170,31746462732,312755404818,3105750620772,31054695744570,
%U A235348 312404601250644,3159598296022978,32108181705850860,327682918265502002,3357089384702757276
%N A235348 Series reversion of x*(1-2*x-5*x^2)/(1-x^2).
%C A235348 Sum of turbulence series A107841 and A235347.
%H A235348 Fung Lam, <a href="/A235348/b235348.txt">Table of n, a(n) for n = 1..1000</a>
%F A235348 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
%t A235348 Rest[CoefficientList[InverseSeries[Series[x*(1-2*x-5*x^2)/(1-x^2), {x, 0, 20}], x],x]] (* _Vaclav Kotesovec_, Jan 29 2014 *)
%o A235348 (Python)
%o A235348 # R. J. Mathar, 2023-03-28
%o A235348 class A235348() :
%o A235348     def __init__(self) :
%o A235348         self.a = [1, 2, 12, 82, 636, 5266]
%o A235348     def at(self, n):
%o A235348         if n <= len(self.a):
%o A235348             return self.a[n-1]
%o A235348         else:
%o A235348             rhs = -3*(n-1)*(160*n-237)*self.at(n-1) \
%o A235348             +3*(-422*n**2+1721*n-1713)*self.at(n-2) \
%o A235348             +2*(-67*n**2+388*n-552)*self.at(n-3) \
%o A235348             +(137*n**2-1352*n+3279)*self.at(n-4) \
%o A235348             +(7*n-37)*(n-6)*self.at(n-5) -(n-6)*(n-7)*self.at(n-6)
%o A235348             rhs //= (-54*n*(n-1))
%o A235348             self.a.append(rhs)
%o A235348             return self.a[-1]
%o A235348 a235348 = A235348()
%o A235348 for n in range(1,12):
%o A235348     print(a235348.at(n))
%o A235348 # a235348.
%o A235348 (PARI) Vec( serreverse(x*(1-2*x-5*x^2)/(1-x^2) +O(x^66) ) ) \\ _Joerg Arndt_, Jan 14 2014
%K A235348 nonn,easy
%O A235348 1,2
%A A235348 _Fung Lam_, Jan 13 2014