A104688 Binomial transform of Moebius sequence.

1, 0, -2, -5, -10, -18, -30, -48, -77, -127, -213, -351, -551, -817, -1181, -1819, -3304, -7003, -15454, -32185, -59830, -94733, -116204, -70931, 138782, 634477, 1440741, 2129014, 995270, -6559829, -30802323, -91672920, -223074852, -473661244, -893720326, -1483495634, -2049478628

Offset

1,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Formula

G.f. A(x) satisfies x = Sum_{n>=1} A( x^n/(1 + x^n) ). - Paul D. Hanna, Jun 03 2025

Example

G.f.: A(x) = x - 2*x^3 - 5*x^4 - 10*x^5 - 18*x^6 - 30*x^7 - 48*x^8 - 77*x^9 - 127*x^10 - 213*x^11 - 351*x^12 + ...

Mathematica

Table[Sum[Binomial[n-1, k-1]*MoebiusMu[k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Jun 01 2025 *)

Crossrefs

Cf. A008683, A124839.

Sequence in context: A025223 A348919 A177787 * A117485 A084835 A298107

Adjacent sequences: A104685 A104686 A104687 * A104689 A104690 A104691

Keyword

sign

Author

Gary W. Adamson, Apr 26 2005

Status

approved