OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 02 2021
STATUS
approved