A348903 G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x - x * A(2*x)).

1, 3, 15, 123, 1623, 35427, 1349727, 94653195, 12690736167, 3325408581747, 1722610175806383, 1774299723226774683, 3644417103927252697335, 14949404433893216347632003, 122555228634241017164802041343, 2008680242472430855727593100321067

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ c * 2^(n*(n-1)/2), where c = 6*Product_{j>=1} (2^j+1)/(2^j-1) = 49.5359276146695003932648450...

a(0) = 1; a(n) = 2 * a(n-1) + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1). - Ilya Gutkovskiy, Nov 03 2021

Mathematica

nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - 2*x - x*A[2*x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A348857, A348860, A348875, A348901, A348904.

Sequence in context: A160884 A173468 A197505 * A191371 A113077 A251661

Adjacent sequences: A348900 A348901 A348902 * A348904 A348905 A348906

Keyword

nonn

Author

Vaclav Kotesovec, Nov 03 2021

Status

approved