A351188 G.f. A(x) satisfies: A(x) = x + x^3 * A(x/(1 + x)) / (1 + x).

0, 1, 0, 0, 1, -2, 3, -3, -2, 24, -94, 280, -687, 1270, -655, -9306, 65087, -306724, 1202250, -4033365, 10855578, -15470865, -69819687, 850568716, -5679272040, 30749200898, -144912453016, 593521998765, -1956641103972, 3349999455415, 20123433921282, -295760693980981

Offset

0,6

Comments

Shifts 3 places left under inverse binomial transform.

Links

Table of n, a(n) for n=0..31.

Formula

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

Mathematica

nmax = 31; A[_] = 0; Do[A[x_] = x + x^3 A[x/(1 + x)]/(1 + x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[1] = 1; a[2] = 0; 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}]

Crossrefs

Cf. A000997, A010741, A351189.

Sequence in context: A155688 A215490 A153592 * A153878 A118925 A308100

Adjacent sequences: A351185 A351186 A351187 * A351189 A351190 A351191

Keyword

sign

Author

Ilya Gutkovskiy, Feb 04 2022

Status

approved