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

%I

%S 1,2,12,82,636,5266,45684,409706,3768132,35346082,336854844,

%T 3252391170,31746462732,312755404818,3105750620772,31054695744570,

%U 312404601250644,3159598296022978,32108181705850860,327682918265502002,3357089384702757276

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

%C Sum of turbulence series A107841 and A235347.

%H Fung Lam, <a href="/A235348/b235348.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 (Python)

%o # a235348. The list a has been calculated (len(a)>=3)

%o m = len(a)

%o if m%2 ==0:

%o ....b = (a[m/2-1])**2

%o else:

%o ....b = 0

%o d = 0

%o for i in range (1,m+3):

%o ....for j in range (1,m+3):

%o ........if (i+j)%m ==0 and (i+j) <= m and i!=j:

%o ............d = d + a[i-1]*a[j-1]

%o f = 0

%o for i in range (1,m+1):

%o ....for j in range (1,m+1):

%o ........if (i+j)%(m+1) ==0 and (i+j) <= (m+1):

%o ............f = f + a[i-1]*a[j-1]

%o g = 0

%o for i in range (1,m+1):

%o ....for j in range (1,m+1):

%o ........for k in range (1,m+1):

%o ............if (i+j+k)%(m+1) ==0 and (i+j+k) <= (m+1):

%o g = g + a[i-1]*a[j-1]*a[k-1]

%o y = 5*g + 2*f - b - d

%o # a235348.

%o (PARI) Vec( serreverse(x*(1-2*x-5*x^2)/(1-x^2) +O(x^66) ) ) \\ _Joerg Arndt_, Jan 14 2014

%K nonn,easy

%O 1,2

%A _Fung Lam_, Jan 13 2014

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Last modified May 21 08:44 EDT 2022. Contains 353908 sequences. (Running on oeis4.)