A349012 G.f. A(x) satisfies: A(x) = (1 + x * A(2*x)) / (1 - x * A(x)).

1, 2, 8, 52, 552, 10208, 350112, 23159760, 3012389984, 777296223040, 399542726439936, 409933997609848192, 840366306053838941952, 3443822768422065940362240, 28218687132517064788995222528, 462391421142204650963524251763968, 15152566983759983965941543133445666304

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

a(n) ~ c * 2^(n*(n-1)/2), where c = 11.40022022373995418911523299051117421707893086825818379118899572625286143... - Vaclav Kotesovec, Nov 06 2021

Mathematica

nmax = 16; A[_] = 0; Do[A[x_] = (1 + x A[2 x])/(1 - x A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = 2^(n - 1) a[n - 1] + Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

Crossrefs

Cf. A006318, A047891, A135867, A348875, A349013.

Sequence in context: A151879 A191552 A154828 * A057629 A191507 A378400

Adjacent sequences: A349009 A349010 A349011 * A349013 A349014 A349015

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 05 2021

Status

approved