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A346052 G.f. A(x) satisfies: A(x) = 1 + x + x^3 * A(x/(1 - x)) / (1 - x).

%I A346052 #9 Nov 30 2022 08:25:09
%S A346052 1,1,0,1,2,3,5,11,29,80,222,630,1881,6004,20420,72979,270659,1035590,
%T A346052 4087205,16675630,70440641,307933393,1390117953,6462787357,
%U A346052 30871458702,151298796000,760250325004,3915477534861,20662363081756,111662169790416,617482470676567,3490973387652861
%N A346052 G.f. A(x) satisfies: A(x) = 1 + x + x^3 * A(x/(1 - x)) / (1 - x).
%H A346052 G. C. Greubel, <a href="/A346052/b346052.txt">Table of n, a(n) for n = 0..650</a>
%F A346052 a(0) = a(1) = 1, a(2) = 0; a(n) = Sum_{k=0..n-3} binomial(n-3,k) * a(k).
%t A346052 nmax = 31; A[_] = 0; Do[A[x_] = 1 + x + x^3 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A346052 a[0] = a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[Binomial[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 31}]
%o A346052 (Magma)
%o A346052 function a(n) // a = A346052
%o A346052   if n lt 3 then return Floor((3-n)/2);
%o A346052   else return (&+[Binomial(n-3,j)*a(j): j in [0..n-3]]);
%o A346052   end if; return a;
%o A346052 end function;
%o A346052 [a(n): n in [0..35]]; // _G. C. Greubel_, Nov 30 2022
%o A346052 (SageMath)
%o A346052 @CachedFunction
%o A346052 def a(n): # a = A346052
%o A346052     if (n<3): return (1, 1, 0)[n]
%o A346052     else: return sum(binomial(n-3, k)*a(k) for k in range(n-2))
%o A346052 [a(n) for n in range(51)] # _G. C. Greubel_, Nov 30 2022
%Y A346052 Cf. A000994, A000995, A000996, A000997, A000998, A007476, A210540, A346050, A346051.
%K A346052 nonn
%O A346052 0,5
%A A346052 _Ilya Gutkovskiy_, Jul 02 2021