A363643 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^3.
0, 1, 3, 7, 10, 22, 21, 53, 45, 126, 55, 373, 78, 764, 390, 2009, 136, 5995, 171, 12501, 5334, 28392, 253, 92353, 1550, 160070, 79110, 394913, 406, 1167406, 465, 2081649, 1083126, 4457010, 69650, 14534659, 666, 22414016, 13818246, 53200481, 820, 158661826, 903
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(#-2) * Binomial[#, 2] &]; Array[a, 50] (* Amiram Eldar, Jul 18 2023 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(d-2)*binomial(d, 2));
Formula
a(n) = Sum_{d|n} (n/d)^(d-2) * binomial(d,2).