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Expansion of Sum_{k>0} (1/(1-x^k)^3 - 1).
5

%I #13 Jul 05 2023 01:45:22

%S 3,9,13,24,24,47,39,69,68,96,81,153,108,165,170,222,174,292,213,342,

%T 302,363,303,523,375,492,474,615,468,766,531,783,686,810,726,1101,744,

%U 999,938,1248,906,1402,993,1413,1306,1437,1179,1901,1314,1773,1562,1938,1488,2238,1698

%N Expansion of Sum_{k>0} (1/(1-x^k)^3 - 1).

%F G.f.: Sum_{k>0} binomial(k+2,2) * x^k/(1 - x^k).

%F a(n) = Sum_{d|n} binomial(d+2,2).

%t a[n_] := DivisorSum[n, Binomial[# + 2, 2] &]; Array[a, 50] (* _Amiram Eldar_, Jul 05 2023 *)

%o (PARI) a(n) = sumdiv(n, d, binomial(d+2, 2));

%Y Cf. A007503, A116963.

%Y Cf. A007437, A069153, A363610.

%K nonn,easy

%O 1,1

%A _Seiichi Manyama_, Jun 12 2023