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A235351 Series reversion of x*(1-3*x-2*x^2)/(1-x).

%I A235351 #24 Sep 04 2024 10:52:48
%S A235351 0,1,2,12,84,660,5548,48836,444412,4147220,39471436,381671204,
%T A235351 3738957148,37028943860,370123733932,3729092573060,37831802166076,
%U A235351 386135110256852,3962278590508812,40852572573083364,423006921400424988,4396894566694687924
%N A235351 Series reversion of x*(1-3*x-2*x^2)/(1-x).
%C A235351 Derived turbulence series: combined series reversion of A107841 and A235349.
%H A235351 Fung Lam, <a href="/A235351/b235351.txt">Table of n, a(n) for n = 0..950</a>
%F A235351 G.f.: (exp(4*Pi*i/3)*u + exp(2*Pi*i/3)*v - 1/2)/x, where i=sqrt(-1),
%F A235351 u = 1/6*(-54-81*x+3*sqrt(-51+522*x+549*x^2-24*x^3))^(1/3), and
%F A235351 v = 1/6*(-54-81*x-3*sqrt(-51+522*x+549*x^2-24*x^3))^(1/3).
%F A235351 D-finite with recurrence 17*n*(n+1)*(11*n-17)*a(n) -n*(1914*n^2-3915*n+1513)*a(n-1) +(-2013*n^3+7137*n^2-7924*n+2640)*a(n-2) +4*(2*n-5)*(11*n-6)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Jun 14 2016
%o A235351 (Python)
%o A235351 a = [0, 1]
%o A235351 for n in range(20):
%o A235351     m = len(a)
%o A235351     d = 0
%o A235351     for i in range (1, m):
%o A235351         for j in range (1, m):
%o A235351             if (i+j)%m ==0 and (i+j) <= m:
%o A235351                 d = d + a[i]*a[j]
%o A235351     g = 0
%o A235351     for i in range (1, m):
%o A235351         for j in range (1, m):
%o A235351             for k in range (1, m):
%o A235351                 if (i+j+k)%m ==0 and (i+j+k) <= m:
%o A235351                     g = g + a[i]*a[j]*a[k]
%o A235351     y = 2*g + 3*d - a[m-1]
%o A235351     a.append(y)
%o A235351 print(a)
%o A235351 (PARI)
%o A235351 my(x='x+O('x^25)); concat([0],Vec(serreverse(x*(1-3*x-2*x^2)/(1-x)))) \\ _Joerg Arndt_, Sep 01 2024
%Y A235351 Cf. A107841, A235349.
%K A235351 nonn,easy
%O A235351 0,3
%A A235351 _Fung Lam_, Jan 16 2014
%E A235351 a(0) = 0 prepended by _Andrey Zabolotskiy_, Aug 31 2024