A337513 - OEIS

%I #5 Aug 30 2020 07:12:41

%S 1,-1,0,1,0,-1,-5,13,5,-43,4,98,122,-638,-246,2912,-537,-9419,-1648,

%T 47005,2243,-232237,87988,904267,-351692,-4123026,1726126,20257940,

%U -14035151,-86846040,73352891,387126945,-358259621,-1853868355,2081413376

%N G.f. A(x) satisfies: A(x) = 1 - Sum_{k=1..4} (x * A(x))^k.

%F G.f.: A(x) = (1/x) * Series_Reversion(x / (1 - x - x^2 - x^3 - x^4)).

%t nmax = 34; A[_] = 0; Do[A[x_] = 1 - Sum[(x A[x])^k, {k, 1, 4}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%t nmax = 35; CoefficientList[(1/x) InverseSeries[Series[x/(1 - x - x^2 - x^3 - x^4), {x, 0, nmax}], x], x]

%t b[m_, r_, k_] := b[m, r, k] = If[m + r == 0, 1, Sum[b[m - j, r + j - 1, k], {j, 1, Min[1, m]}] - Sum[b[m + j - 1, r - j, k], {j, 1, Min[k, r]}]]; a[n_] := b[0, n, 4]; Table[a[n], {n, 0, 34}]

%Y Cf. A000078, A007440, A036766, A337512, A337514.

%K sign

%O 0,7

%A _Ilya Gutkovskiy_, Aug 30 2020