A352865 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-k,k) * a(n-2*k-1).

1, 1, 1, -1, -4, -5, 6, 36, 46, -101, -515, -506, 2554, 9991, 3067, -79915, -227056, 205681, 2841708, 5134140, -18296153, -107927240, -66578269, 1174691649, 4059143386, -4667894370, -69377504739, -126787267800, 669710503012, 3835079736835, 475781902203

Offset: 0

Author

Ilya Gutkovskiy, Apr 06 2022

Keywords

• sign

Crossrefs

Cf. A014619, A172385, A352864.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - k, 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 + x A[x/(1 + x^2)]/(1 + x^2)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]

Formula

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