A349013 G.f. A(x) satisfies: A(x) = (1 + x * A(2*x)) / (1 - x^2 * A(x)).

1, 1, 3, 14, 119, 1938, 62291, 3990822, 510954584, 130812494690, 66977027614263, 68584738950054184, 140461679588587238360, 575331176899085656611498, 4713113282218244019907299347, 77219649166807400596911172015640, 2530333473325322974256848862067093128

Offset

0,3

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-2} a(k) * a(n-k-2).

a(n) ~ c * 2^(n*(n-1)/2), where c = 1.903611332661849505687584024897203124045921097899485586512432930506328189... - Vaclav Kotesovec, Nov 06 2021

Mathematica

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

Crossrefs

Cf. A000108, A001006, A135867, A348878, A349012.

Sequence in context: A007140 A161936 A304983 * A260887 A127850 A324147

Adjacent sequences: A349010 A349011 A349012 * A349014 A349015 A349016

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 05 2021

Status

approved