A363651 Expansion of Sum_{k>0} x^(2*k)/(1 - (k*x)^k)^3.
0, 1, 3, 7, 10, 28, 21, 125, 117, 686, 55, 9049, 78, 21596, 206310, 508025, 136, 8701561, 171, 229315221, 303797886, 14418152, 253, 88452515089, 305175781550, 327156038, 377734977126, 27160609347425, 406, 2458857416866336, 465, 9570181420417521
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(n-2*n/#) * Binomial[#, 2] &]; Array[a, 33] (* Amiram Eldar, Jul 18 2023 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(n-2*n/d)*binomial(d, 2));
Formula
a(n) = Sum_{d|n} (n/d)^(n-2*n/d) * binomial(d,2).