A103448 a(n) = Sum_{k=0..n} Moebius(binomial(n,k)).

1, 2, 1, 0, 3, 2, 6, 4, 1, 2, 6, 4, 0, -6, 8, 6, 2, -2, 2, -4, 4, 10, 4, 8, 0, 4, 8, 2, 4, 0, -2, -4, 2, 4, 0, 4, 2, -4, 10, 4, 0, -8, 6, -2, 4, -4, 8, 2, 2, 2, 2, 4, 6, 2, 0, 6, 2, 2, 2, -6, 0, 6, 4, 8, 2, 4, 2, 0, 0, 8, -4, -2, 2, 4, 2, 0, -2, 14, 10, -2, 2, 2, 4, 2, 4, -2, 0, 8, 4, 2, 2, -2, 6, 0, -6, 14, 2, 0, 2, 2, 2, 4, 0, 2, -2

Offset

0,2

Comments

Row sums of A103447.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} Moebius(binomial(n,k)).

a(n) = Sum_{k=0..n} A008683(A007318(n,k)).

Example

a(4)=3 because mu(1) + mu(4) + mu(6) + mu(4) + mu(1) = 1 + 0 + 1 + 0 + 1 = 3.

Mathematica

Table[Sum[MoebiusMu[Binomial[n, k]], {k, 0, n}], {n, 0, 120}] (* G. C. Greubel, Jun 16 2021 *)

Prog

(Magma) [(&+[ MoebiusMu(Binomial(n, k)): k in [0..n]]): n in [0..120]]; // G. C. Greubel, Jun 16 2021
(Sage) [sum(moebius(binomial(n, k)) for k in (0..n)) for n in (0..120)] # G. C. Greubel, Jun 16 2021
(PARI) a(n) = sum(k=0, n, moebius(binomial(n, k))); \\ Michel Marcus, Jun 17 2021

Crossrefs

Cf. A007318, A008683, A103447, A103449.

Sequence in context: A072661 A103432 A334374 * A186904 A216216 A078803

Adjacent sequences: A103445 A103446 A103447 * A103449 A103450 A103451

Keyword

sign

Author

Emeric Deutsch, Feb 07 2005

Status

approved