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A352010
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-3)^k * a(k) * a(n-2*k-1).
2
1, 1, 1, -2, -5, 1, 16, 94, 127, -317, -1103, -2258, 160, 18922, 39664, -163064, -524489, -187577, 1711591, 12353800, 18926119, -53449661, -207918068, -15689834, 960812728, 3295064650, 3870965368, -33248209286, -96830084768, 17122290256, 505711364524
OFFSET
0,4
FORMULA
G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(-3*x^2)).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[(-3)^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 30}]
nmax = 30; A[_] = 0; Do[A[x_] = 1/(1 - x A[-3 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Feb 28 2022
STATUS
approved