A363974 Expansion of Sum_{k>0} x^k / (1 - x^(2*k))^3.

1, 1, 4, 1, 7, 4, 11, 1, 19, 7, 22, 4, 29, 11, 46, 1, 46, 19, 56, 7, 80, 22, 79, 4, 98, 29, 124, 11, 121, 46, 137, 1, 178, 46, 188, 19, 191, 56, 242, 7, 232, 80, 254, 22, 337, 79, 301, 4, 336, 98, 400, 29, 379, 124, 434, 11, 494, 121, 466, 46, 497, 137, 623, 1, 596, 178, 596, 46, 712, 188, 667, 19

Offset

1,3

Links

Table of n, a(n) for n=1..72.

Formula

G.f.: Sum_{k>0} k*(k+1)/2 * x^(2*k-1) / (1 - x^(2*k-1)).

a(n) = Sum_{d|n, d==1 mod 2} binomial((d+1)/2+1,2).

Mathematica

a[n_] := DivisorSum[n, Binomial[(#+1)/2+1, 2] &, OddQ[#] &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

Prog

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

Crossrefs

Cf. A001227, A113415.

Cf. A363969.

Sequence in context: A019651 A262606 A286387 * A342633 A094649 A344970

Adjacent sequences: A363971 A363972 A363973 * A363975 A363976 A363977

Keyword

nonn

Author

Seiichi Manyama, Jun 30 2023

Status

approved