A348877 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(4*x)).

1, 2, 12, 232, 15792, 4108192, 4223439552, 17316156716672, 283777228606348032, 18598759772257600748032, 4875627680189345535622228992, 5112485673116229482189477259405312, 21443339558695300334256395183459423465472, 359759625310995318218730673236935427042834358272

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = 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 = 2*Product_{j>=1} (4^j+1)/(4^j-1) = 3.938520707336538863894387393934531340132379924622409970534801850699757421... - Vaclav Kotesovec, Nov 03 2021

Mathematica

nmax = 13; A[_] = 0; Do[A[x_] = 1/(1 - x - x A[4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := 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. A006318, A015085, A348875, A348876.

Sequence in context: A009359 A011807 A182507 * A309615 A166316 A011840

Adjacent sequences: A348874 A348875 A348876 * A348878 A348879 A348880

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2021

Status

approved