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A343546
a(n) = n * Sum_{d|n} binomial(d+4,5)/d.
4
1, 8, 24, 72, 131, 318, 469, 936, 1359, 2294, 3014, 5172, 6201, 9548, 12126, 17376, 20366, 29862, 33668, 47372, 54684, 71874, 80753, 111000, 119410, 154986, 173988, 220864, 237365, 309864, 324663, 411744, 445170, 542776, 578984, 731340, 749435, 918118, 981474
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} k * x^k/(1 - x^k)^6 = Sum_{k>=1} binomial(k+4,5) * x^k/(1 - x^k)^2.
MATHEMATICA
a[n_] := n * DivisorSum[n, Binomial[# + 4, 5]/# &]; Array[a, 40] (* Amiram Eldar, Apr 25 2021 *)
PROG
(PARI) a(n) = n*sumdiv(n, d, binomial(d+4, 5)/d);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+4, 5)*x^k/(1-x^k)^2))
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 19 2021
STATUS
approved