A363639 Expansion of Sum_{k>0} (1/(1 - k*x^k)^3 - 1).

3, 12, 19, 51, 36, 180, 57, 405, 352, 918, 111, 3990, 144, 5064, 6534, 15945, 222, 51462, 267, 99354, 82478, 160812, 369, 808490, 66051, 861630, 1090342, 2593614, 552, 8966414, 621, 13039761, 13831470, 22415778, 3166218, 114011229, 852, 110103540, 167426822

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Formula

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + 2, 2] &]; Array[a, 40] (* Amiram Eldar, Jul 17 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^d*binomial(d+2, 2));

Crossrefs

Cf. A338662, A362683, A363640.

Cf. A363642, A363643, A363644.

Cf. A363628, A363647.

Sequence in context: A134965 A117554 A049714 * A199129 A257942 A063244

Adjacent sequences: A363636 A363637 A363638 * A363640 A363641 A363642

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved