A343545 - OEIS

%I #14 Apr 25 2021 02:22:40

%S 1,7,18,49,75,177,217,428,549,890,1012,1824,1833,2849,3360,4732,4862,

%T 7506,7334,10810,11382,14729,14973,22188,20850,27482,29052,37408,

%U 35989,50490,46407,61824,62106,75854,75390,101673,91427,116033,117624,146680,135792,179886,163228,208208

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

%F 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.

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

%o (PARI) a(n) = n*sumdiv(n, d, binomial(d+3, 4)/d);

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

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

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 19 2021