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A363643 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^3.

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%I A363643 #13 Jul 19 2023 02:19:17
%S A363643 0,1,3,7,10,22,21,53,45,126,55,373,78,764,390,2009,136,5995,171,12501,
%T A363643 5334,28392,253,92353,1550,160070,79110,394913,406,1167406,465,
%U A363643 2081649,1083126,4457010,69650,14534659,666,22414016,13818246,53200481,820,158661826,903
%N A363643 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^3.
%F A363643 a(n) = Sum_{d|n} (n/d)^(d-2) * binomial(d,2).
%t A363643 a[n_] := DivisorSum[n, (n/#)^(#-2) * Binomial[#, 2] &]; Array[a, 50] (* _Amiram Eldar_, Jul 18 2023 *)
%o A363643 (PARI) a(n) = sumdiv(n, d, (n/d)^(d-2)*binomial(d, 2));
%Y A363643 Cf. A363639, A363642, A363644.
%Y A363643 Cf. A363651.
%K A363643 nonn
%O A363643 1,3
%A A363643 _Seiichi Manyama_, Jun 13 2023