A362021 a(n) = Sum_{k=1..n} (-1)^(n-k) * k * mu(k), where mu(k) is the Moebius function.

1, -3, 0, 0, -5, 11, -18, 18, -18, 28, -39, 39, -52, 66, -51, 51, -68, 68, -87, 87, -66, 88, -111, 111, -111, 137, -137, 137, -166, 136, -167, 167, -134, 168, -133, 133, -170, 208, -169, 169, -210, 168, -211, 211, -211, 257, -304, 304, -304, 304, -253, 253, -306, 306, -251, 251, -194, 252, -311

Offset: 1

Author

Seiichi Manyama, Apr 04 2023

Keywords

• sign
• easy
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008683, A055615, A068340, A247418, A361982.

Programs

PARI

a(n) = sum(k=1, n, (-1)^(n-k)*k*moebius(k));

Formula

G.f.: (Sum_{k>=1} k * mu(k) * x^k) / (1 + x).

G.f. A(x) satisfies x = Sum_{k>=1} k * (1 + x^k) * A(x^k).

a(n) = -a(n-1) + A055615(n) for n > 1.