A343546 - OEIS

%I #13 Apr 25 2021 02:22:34

%S 1,8,24,72,131,318,469,936,1359,2294,3014,5172,6201,9548,12126,17376,

%T 20366,29862,33668,47372,54684,71874,80753,111000,119410,154986,

%U 173988,220864,237365,309864,324663,411744,445170,542776,578984,731340,749435,918118,981474

%N a(n) = n * Sum_{d|n} binomial(d+4,5)/d.

%F 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.

%t a[n_] := n * DivisorSum[n, Binomial[# + 4, 5]/# &]; Array[a, 40] (* _Amiram Eldar_, Apr 25 2021 *)

%o (PARI) a(n) = n*sumdiv(n, d, binomial(d+4, 5)/d);

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+4, 5)*x^k/(1-x^k)^2))

%Y Cf. A000203, A038040, A101289, A309731, A343544, A343545, A343547.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 19 2021