A348876 - OEIS

%I #9 Nov 03 2021 04:40:49

%S 1,2,10,122,3778,321794,79518154,58289895290,127713856067074,

%T 838441945709583746,16506407616569722560778,

%U 974752895709158578160969978,172678450359956040815290930278850,91769099059347441553324620759011469698,146309952397373808216450794120154608358754762

%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).

%F a(n) ~ c * 3^(n*(n-1)/2), where c = 2*Product_{j>=1} (3^j+1)/(3^j-1) = QPochhammer(-1, 1/3) / QPochhammer(1/3) = 5.58779203552209791475992929265... - _Vaclav Kotesovec_, Nov 03 2021

%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, A015084, A348875, A348877.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Nov 02 2021