A363608 Expansion of Sum_{k>0} x^(4*k)/(1-x^k)^5.

0, 0, 0, 1, 5, 15, 35, 71, 126, 215, 330, 511, 715, 1036, 1370, 1891, 2380, 3201, 3876, 5061, 6020, 7645, 8855, 11207, 12655, 15665, 17676, 21512, 23751, 29000, 31465, 37851, 41250, 48756, 52400, 62602, 66045, 77691, 82966, 96521, 101270, 118966, 123410, 143397

Offset

1,5

Links

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

Formula

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

a(n) = Sum_{d|n} binomial(d,4).

Mathematica

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

Prog

(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)))

Crossrefs

Cf. A000203, A069153, A363607.

Sequence in context: A019499 A229885 A363618 * A243739 A145133 A270784

Adjacent sequences: A363605 A363606 A363607 * A363609 A363610 A363611

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 11 2023

Status

approved