A363644 - OEIS

%I #13 Jul 19 2023 02:19:21

%S 0,0,1,3,6,11,15,27,29,60,45,145,66,318,146,789,120,2199,153,4890,

%T 1406,11730,231,34175,426,67884,20738,163956,378,453341,435,882153,

%U 295742,1966608,10230,5656484,630,10027674,3897938,23069916,780,63648517,861,113050536

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

%F a(n) = Sum_{d|n} (n/d)^(d-3) * binomial(d-1,2).

%t a[n_] := DivisorSum[n, (n/#)^(# - 3)*Binomial[# - 1, 2] &]; Array[a, 50] (* _Amiram Eldar_, Jul 18 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (n/d)^(d-3)*binomial(d-1, 2));

%Y Cf. A363639, A363642, A363643.

%Y Cf. A363610, A363652.

%K nonn

%O 1,4

%A _Seiichi Manyama_, Jun 13 2023