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A349032
G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-2*x)).
2
1, 2, 0, -8, 48, 1024, -29376, -2008960, 249483264, 64889376256, -32966832018432, -33890678261809152, 69272943033878630400, 284019472607289480388608, -2325552273529676473281282048, -38111154065733485540332985155584, 1248673879720871231428642700812025856
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-2)^k * a(k) * a(n-k-1).
MATHEMATICA
nmax = 16; A[_] = 0; Do[A[x_] = 1/(1 - x - x A[-2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := 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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 06 2021
STATUS
approved