%I #16 Jul 25 2023 17:29:53

%S 0,1,5,16,35,76,126,226,335,531,715,1092,1365,1947,2420,3286,3876,

%T 5251,5985,7861,8986,11342,12650,16252,17585,21841,24086,29367,31465,

%U 38946,40920,49662,53080,62782,66206,80082,82251,97376,102640,120001,123410,146628

%N Expansion of Sum_{k>0} x^(2*k)/(1-x^k)^5.

%H Seiichi Manyama, <a href="/A363605/b363605.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>0} binomial(k+2,4) * x^k/(1 - x^k).

%F a(n) = Sum_{d|n} binomial(d+2,4).

%t a[n_] := DivisorSum[n, Binomial[# + 2, 4] &]; Array[a, 40] (* _Amiram Eldar_, Jul 25 2023 *)

%o (PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1-x^k)^5)))

%Y Cf. A032741, A065608, A069153, A363604, A363606.

%K nonn,easy

%O 1,3

%A _Seiichi Manyama_, Jun 11 2023