A062791 Moebius transform of central binomial coefficients.

1, 1, 2, 4, 9, 16, 34, 64, 123, 241, 461, 900, 1715, 3396, 6423, 12800, 24309, 48477, 92377, 184500, 352679, 704969, 1352077, 2703168, 5200290, 10398883, 20058174, 40113164, 77558759, 155110827, 300540194, 601067520, 1166802646, 2333581909, 4537567606

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{d|n} A001405(n/d)*mu(d).

Example

n=7, C[7,3]=35, A001405[7/d]={C[7,3],C[1,0]}={35,1}, mu[d]={1,-1}, the sum is a(7)=35-1=34.

Maple

with(numtheory):
a:= n-> add(binomial(d, iquo(d, 2))*mobius(n/d), d=divisors(n)):
seq(a(n), n=1..40);  # Alois P. Heinz, Jul 09 2017

Crossrefs

Cf. A001405.

Sequence in context: A302831 A091437 A131337 * A203320 A005980 A128093

Adjacent sequences: A062788 A062789 A062790 * A062792 A062793 A062794

Keyword

nonn

Author

Labos Elemer, Jul 19 2001

Extensions

Offset corrected by Eric Rowland, Jul 09 2017

Status

approved