A348858 - OEIS

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A348858

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

1, 2, 9, 103, 3101, 261192, 64285189, 47059492688, 103060910397021, 676492249628112382, 13317427360663454672669, 786420726604930579016189223, 139314431838014895142151741877241, 74037818920801629179455290512454633872, 118040419689979917511971388549088825283510249

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

FORMULA

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 = 4.508135635010167805309616576501854361005320931661829410476785686203732753... - Vaclav Kotesovec, Nov 02 2021

MATHEMATICA

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]

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

CROSSREFS