A348857 G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(2*x))).

1, 2, 7, 44, 481, 9254, 326395, 21927776, 2874607189, 744650622170, 383510575423471, 393869218949592212, 807827718206737362889, 3311287802485779192925838, 27136007596894473408507305443, 444677773080105539125038867872456, 14572535437424416878539776253365375549

Offset

0,2

Links

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

Formula

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

a(n) ~ c * 2^(n*(n-1)/2), where c = 10.96416094535958612421479005398505892527943513193882801485045169159164... - Vaclav Kotesovec, Nov 02 2021

Mathematica

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

Crossrefs

Cf. A007317, A015083, A348858, A348859.

Sequence in context: A242105 A001046 A158257 * A172389 A153522 A355109

Adjacent sequences: A348854 A348855 A348856 * A348858 A348859 A348860

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2021

Status

approved