A348861 - OEIS

%I #7 Nov 02 2021 09:51:44

%S 1,0,1,9,253,20754,5064301,3696964686,8088964208893,53079786931826952,

%T 1044822534120774924517,61696770693051062357722413,

%U 10929459535778338593167921597497,5808373834674826377471903826388912406,9260429805605038398327449254849233420999649

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

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

%F a(n) ~ c * 3^(n*(n-1)/2), where c = 0.353669086629957226916356822657293915192042094460583129054709983118948... - _Vaclav Kotesovec_, Nov 02 2021

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

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

%Y Cf. A005043, A015084, A348860, A348862.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Nov 02 2021