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a(n) = Sum_{d|n} mu(n/d) * binomial(d,4).
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%I #4 Aug 02 2021 07:55:28

%S 0,0,0,1,5,15,35,69,126,205,330,479,715,966,1360,1750,2380,2919,3876,

%T 4634,5950,6985,8855,10062,12645,14235,17424,19473,23751,25820,31465,

%U 34140,40590,43996,52320,55365,66045,69939,81536,86476,101270,104964,123410,128435,147504

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

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

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

%t Table[Sum[MoebiusMu[n/d] Binomial[d, 4], {d, Divisors[n]}], {n, 1, 45}]

%t nmax = 45; CoefficientList[Series[Sum[MoebiusMu[k] x^(4 k)/(1 - x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y 4th column of A020921.

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

%K nonn

%O 1,5

%A _Ilya Gutkovskiy_, Aug 02 2021