A346761 a(n) = Sum_{d|n} mu(n/d) * binomial(d,4).

0, 0, 0, 1, 5, 15, 35, 69, 126, 205, 330, 479, 715, 966, 1360, 1750, 2380, 2919, 3876, 4634, 5950, 6985, 8855, 10062, 12645, 14235, 17424, 19473, 23751, 25820, 31465, 34140, 40590, 43996, 52320, 55365, 66045, 69939, 81536, 86476, 101270, 104964, 123410, 128435, 147504

Offset

1,5

Links

Table of n, a(n) for n=1..45.

Formula

G.f.: Sum_{k>=1} mu(k) * x^(4*k) / (1 - x^k)^5.

a(n) = (A059377(n) - 6 * A059376(n) + 11 * A007434(n) - 6 * A000010(n)) / 24.

Mathematica

Table[Sum[MoebiusMu[n/d] Binomial[d, 4], {d, Divisors[n]}], {n, 1, 45}]
nmax = 45; CoefficientList[Series[Sum[MoebiusMu[k] x^(4 k)/(1 - x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

4th column of A020921.

Cf. A000010, A000332, A007434, A059376, A059377, A102309, A117109, A346760.

Sequence in context: A005894 A374711 A015622 * A374714 A341134 A292103

Adjacent sequences: A346758 A346759 A346760 * A346762 A346763 A346764

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved