OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x * A(2*x/(1 - x)) / (1 - x)^2.
a(n) ~ c * 2^(n*(n-1)/2), where c = 8.12511731924148105991770742530352144084320407825344... - Vaclav Kotesovec, Apr 07 2022
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k + 1] 2^k a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; A[_] = 0; Do[A[x_] = 1 + x A[2 x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2022
STATUS
approved