A348876 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(3*x)).

1, 2, 10, 122, 3778, 321794, 79518154, 58289895290, 127713856067074, 838441945709583746, 16506407616569722560778, 974752895709158578160969978, 172678450359956040815290930278850, 91769099059347441553324620759011469698, 146309952397373808216450794120154608358754762

Offset: 0

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

• nonn

Crossrefs

Cf. A006318, A015084, A348875, A348877.

Programs

Mathematica

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]
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}]

Formula

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

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