A363644 Expansion of Sum_{k>0} x^(3*k)/(1 - k*x^k)^3.

0, 0, 1, 3, 6, 11, 15, 27, 29, 60, 45, 145, 66, 318, 146, 789, 120, 2199, 153, 4890, 1406, 11730, 231, 34175, 426, 67884, 20738, 163956, 378, 453341, 435, 882153, 295742, 1966608, 10230, 5656484, 630, 10027674, 3897938, 23069916, 780, 63648517, 861, 113050536

Offset

1,4

Links

Table of n, a(n) for n=1..44.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A363639, A363642, A363643.

Cf. A363610, A363652.

Sequence in context: A131665 A363610 A132158 * A363652 A368586 A310101

Adjacent sequences: A363641 A363642 A363643 * A363645 A363646 A363647

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved