A363640 Expansion of Sum_{k>0} (1/(1 - k*x^k)^4 - 1).

4, 18, 32, 91, 76, 358, 148, 917, 796, 2368, 408, 10354, 612, 16586, 16984, 52873, 1208, 180408, 1616, 374934, 271408, 749070, 2692, 3350370, 178376, 4592968, 4349008, 13197802, 5076, 45402484, 6108, 74470417, 64515400, 149432876, 10324768, 652324677, 10028

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Formula

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + 3, 3] &]; Array[a, 40] (* Amiram Eldar, Jul 17 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^d*binomial(d+3, 3));

Crossrefs

Cf. A338662, A362683, A363639.

Cf. A116963, A363648.

Sequence in context: A130656 A292161 A346866 * A053191 A003474 A337003

Adjacent sequences: A363637 A363638 A363639 * A363641 A363642 A363643

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved