A352011 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-4)^k * a(k) * a(n-2*k-1).

1, 1, 1, -3, -7, 5, 33, 269, 393, -1451, -4815, -14115, -2791, 171685, 398145, -3887699, -10399319, 6567925, 63031889, 558518141, 853157689, -4400392635, -14954126751, 29904043597, 151457170889, 344861133205, 170895616881, -12627954103779, -30049168949927

Offset: 0

Author

Ilya Gutkovskiy, Feb 28 2022

Keywords

• sign

Crossrefs

Cf. A015099, A101912, A352009, A352010.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-4)^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 28}]
nmax = 28; A[] = 0; Do[A[x] = 1/(1 - x A[-4 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(-4*x^2)).