A363645 Expansion of Sum_{k>0} x^k/(1 - k*x^k)^4.

1, 5, 11, 29, 36, 109, 85, 297, 256, 801, 287, 2881, 456, 5965, 3766, 17489, 970, 57385, 1331, 125681, 63498, 294933, 2301, 1072865, 24801, 1867009, 1087030, 4942561, 4496, 15697761, 5457, 28721057, 16895770, 63511593, 1404306, 225177013, 9140, 348661477

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Formula

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^(# - 1)*Binomial[# + 2, 3] &]; Array[a, 40] (* Amiram Eldar, Jul 18 2023 *)

Prog

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

Crossrefs

Cf. A167531, A363642.

Cf. A059358.

Sequence in context: A095053 A291279 A182379 * A243544 A141561 A240103

Adjacent sequences: A363642 A363643 A363644 * A363646 A363647 A363648

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved