OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 2 * x^2 * A'(x)) ).
a(n) ~ c * 2^n * n * n!, where c = 0.6018110636400677977754542011395053310779724922160159... - Vaclav Kotesovec, Sep 11 2024
MATHEMATICA
a[n_] := a[n] = 1 + Sum[(2 k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x] - 2 x^2 A'[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 11 2024
STATUS
approved