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A348903
G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x - x * A(2*x)).
1
1, 3, 15, 123, 1623, 35427, 1349727, 94653195, 12690736167, 3325408581747, 1722610175806383, 1774299723226774683, 3644417103927252697335, 14949404433893216347632003, 122555228634241017164802041343, 2008680242472430855727593100321067
OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 03 2021
STATUS
approved