A343545 a(n) = n * Sum_{d|n} binomial(d+3,4)/d.

1, 7, 18, 49, 75, 177, 217, 428, 549, 890, 1012, 1824, 1833, 2849, 3360, 4732, 4862, 7506, 7334, 10810, 11382, 14729, 14973, 22188, 20850, 27482, 29052, 37408, 35989, 50490, 46407, 61824, 62106, 75854, 75390, 101673, 91427, 116033, 117624, 146680, 135792, 179886, 163228, 208208

Offset

1,2

Links

Table of n, a(n) for n=1..44.

Formula

G.f.: Sum_{k>=1} k * x^k/(1 - x^k)^5 = Sum_{k>=1} binomial(k+3,4) * x^k/(1 - x^k)^2.

Mathematica

a[n_] := n * DivisorSum[n, Binomial[# + 3, 4]/# &]; Array[a, 50] (* Amiram Eldar, Apr 25 2021 *)

Prog

(PARI) a(n) = n*sumdiv(n, d, binomial(d+3, 4)/d);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+3, 4)*x^k/(1-x^k)^2))

Crossrefs

Cf. A000203, A038040, A073570, A309731, A343544, A343546, A343547.

Sequence in context: A124053 A356042 A324900 * A324944 A084819 A346494

Adjacent sequences: A343542 A343543 A343544 * A343546 A343547 A343548

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2021

Status

approved