A348904 G.f. A(x) satisfies: A(x) = 1 / (1 - 3*x - x * A(2*x)).

1, 4, 24, 224, 3264, 76544, 3055104, 220125184, 29946753024, 7906463105024, 4111398632914944, 4242968041649209344, 8723543411935886966784, 35801422714130756942168064, 293571666811153273905871847424, 4812226763497124503879315624034304, 157725544404988739801460227609821446144

Offset: 0

Author

Vaclav Kotesovec, Nov 03 2021

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A348903.

Programs

Mathematica

nmax = 20; A[] = 0; Do[A[x] = 1/(1 - 3*x - x*A[2*x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

a(n) ~ c * 2^(n*(n-1)/2), where c = 118.688483279581472418531869762515593107529867862298434268...

a(0) = 1; a(n) = 3 * a(n-1) + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1). - Ilya Gutkovskiy, Nov 03 2021