A363606 Expansion of Sum_{k>0} x^(2*k)/(1-x^k)^6.

0, 1, 6, 22, 56, 133, 252, 484, 798, 1344, 2002, 3157, 4368, 6441, 8630, 12112, 15504, 21274, 26334, 35014, 42762, 55133, 65780, 84349, 98336, 123124, 143304, 176373, 201376, 247380, 278256, 336744, 379000, 451402, 502250, 600055, 658008, 775733, 855042

Offset

1,3

Links

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

Formula

G.f.: Sum_{k>0} binomial(k+3,5) * x^k/(1 - x^k).

a(n) = Sum_{d|n} binomial(d+3,5).

Mathematica

a[n_] := DivisorSum[n, Binomial[# + 3, 5] &]; Array[a, 40] (* Amiram Eldar, Jul 25 2023 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^k)^6)))

Crossrefs

Cf. A032741, A065608, A069153, A363604, A363605.

Sequence in context: A034134 A081441 A363614 * A366448 A127760 A320243

Adjacent sequences: A363603 A363604 A363605 * A363607 A363608 A363609

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 11 2023

Status

approved