A363618 Expansion of Sum_{k>0} x^(4*k)/(1+x^k)^5.

0, 0, 0, 1, -5, 15, -35, 71, -126, 205, -330, 511, -715, 966, -1370, 1891, -2380, 2949, -3876, 5051, -6020, 6985, -8855, 11207, -12655, 14235, -17676, 21442, -23751, 26260, -31465, 37851, -41250, 43996, -52400, 62350, -66045, 69939, -82966, 96511, -101270

Offset: 1

Author

Seiichi Manyama, Jun 11 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A363022, A363617.

Cf. A363608.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^# * Binomial[#, 4] &]; Array[a, 50] (* Amiram Eldar, Jul 25 2023 *)

PARI

my(N=50, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/(1+x^k)^5)))

PARI

a(n) = sumdiv(n, d, (-1)^d*binomial(d, 4));

Formula

G.f.: Sum_{k>0} binomial(k,4) * (-x)^k/(1 - x^k).

a(n) = Sum_{d|n} (-1)^d * binomial(d,4).