A348858 - OEIS

%I #7 Nov 02 2021 09:50:06

%S 1,2,9,103,3101,261192,64285189,47059492688,103060910397021,

%T 676492249628112382,13317427360663454672669,

%U 786420726604930579016189223,139314431838014895142151741877241,74037818920801629179455290512454633872,118040419689979917511971388549088825283510249

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

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

%F a(n) ~ c * 3^(n*(n-1)/2), where c = 4.508135635010167805309616576501854361005320931661829410476785686203732753... - _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 + Sum[3^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]

%Y Cf. A007317, A015084, A348857, A348859.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Nov 02 2021