A348859 G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(4*x))).

1, 2, 11, 204, 13701, 3550838, 3646912991, 14948746703872, 244965160945456921, 16054771878797715999594, 4208710286900635084866205491, 4413165224136772109314051383922356, 18510169791808150609141704979384516863021, 310549172324407121253872529077196811473762678750

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = 1 + Sum_{k=0..n-1} 4^k * a(k) * a(n-k-1).

a(n) ~ c * 2^(n*(n-1)), where c = 3.399782064170449155365557063612838469541502782488369640092639686931819... - Vaclav Kotesovec, Nov 02 2021

Mathematica

nmax = 13; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[4 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = 1 + Sum[4^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

Crossrefs

Cf. A007317, A015085, A348857, A348858.

Sequence in context: A226052 A271429 A051663 * A358649 A188203 A070256

Adjacent sequences: A348856 A348857 A348858 * A348860 A348861 A348862

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2021

Status

approved