A351189 G.f. A(x) satisfies: A(x) = x^2 + x^3 * A(x/(1 + x)) / (1 + x).

0, 0, 1, 0, 0, 1, -3, 6, -9, 6, 27, -169, 645, -1995, 5122, -9570, 1242, 109739, -756648, 3733128, -15527337, 55626585, -161247102, 260402511, 1028417064, -14243992155, 102551438561, -595149283191, 3010031905815, -13336771020834, 48891499316016, -111677138548476

Offset: 0

Author

Ilya Gutkovskiy, Feb 04 2022

Keywords

• sign

Comments

Shifts 3 places left under inverse binomial transform.

Crossrefs

Cf. A000998, A010741, A351188.

Programs

Mathematica

nmax = 31; A[] = 0; Do[A[x] = x^2 + x^3 A[x/(1 + x)]/(1 + x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 0; a[2] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - 3, k] a[n - k - 3], {k, 0, n - 3}]; Table[a[n], {n, 0, 31}]

Formula

a(0) = a(1) = 0, a(2) = 1; a(n) = Sum_{k=0..n-3} (-1)^k * binomial(n-3,k) * a(n-k-3).