%I #6 Nov 06 2021 20:15:28

%S 1,2,-2,-34,826,70634,-16895162,-12385295242,27037369868722,

%T 177500531682526034,-3493033395457140741746,

%U -206274103942288894158940594,36540013650535335202759969693162,19419007557809179132528500713950083002,-30960092711143410415029705970483650552421802

%N G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-3*x)).

%F a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-3)^k * a(k) * a(n-k-1).

%t nmax = 14; A[_] = 0; Do[A[x_] = 1/(1 - x - x A[-3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%t a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-3)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]

%Y Cf. A006318, A015098, A348876, A349032, A349034.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Nov 06 2021