A363695 - OEIS

%I #19 Jul 05 2023 01:45:16

%S 5,20,40,90,131,265,335,585,755,1147,1370,2155,2385,3410,4042,5430,

%T 5990,8295,8860,11843,13020,16335,17555,23125,23882,29805,32220,39440,

%U 40925,51644,52365,64335,67450,79820,82712,101575,101275,120805,125830,148089,149000,179490

%N Expansion of Sum_{k>0} (1/(1-x^k)^5 - 1).

%H Seiichi Manyama, <a href="/A363695/b363695.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>0} binomial(k+4,4) * x^k/(1 - x^k).

%F a(n) = Sum_{d|n} binomial(d+4,4).

%t a[n_] := DivisorSum[n, Binomial[# + 4, 4] &]; Array[a, 40] (* _Amiram Eldar_, Jul 05 2023 *)

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

%Y Cf. A007503, A116963, A363628, A363696.

%Y Cf. A073570, A363605, A363608.

%K nonn,easy

%O 1,1

%A _Seiichi Manyama_, Jun 16 2023