A363652 Expansion of Sum_{k>0} x^(3*k)/(1 - (k*x)^k)^3.
0, 0, 1, 3, 6, 11, 15, 33, 29, 132, 45, 777, 66, 3918, 4466, 22377, 120, 311655, 153, 992586, 7971806, 2949330, 231, 483657349, 58594026, 69206316, 10847774018, 64754136132, 378, 696335917637, 435, 23096840946129, 12709329142142, 32212255248, 1434580813047030
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(n - 3*n/#)*Binomial[# - 1, 2] &]; Array[a, 35] (* Amiram Eldar, Jul 18 2023 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(n-3*n/d)*binomial(d-1, 2));
Formula
a(n) = Sum_{d|n} (n/d)^(n-3*n/d) * binomial(d-1,2).