A348188 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(3*x)).

1, 1, 7, 139, 7813, 1282741, 626077507, 914089078999, 4000061058178633, 52496811551448519241, 2066694521388276020211487, 244076623554395367965602542499, 86475371441574361841467969073397133, 91913288701991663661449175594278601481981

Offset: 0

Author

Ilya Gutkovskiy, Nov 03 2021

Keywords

• nonn

Crossrefs

Cf. A001003, A015084, A348901, A348902.

Programs

Mathematica

nmax = 13; A[] = 0; Do[A[x] = 1/(1 + x - 2 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] + 2 Sum[3^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

Formula

a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..n-1} 3^k * a(k) * a(n-k-1).

a(n) ~ c * 3^(n*(n-1)/2) * 2^n, where c = 0.68317332785969015770364424102230433743028917778042859282957908502822... - Vaclav Kotesovec, Nov 03 2021