This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363614 #19 Jul 19 2023 02:19:46
%S A363614 0,1,-6,22,-56,121,-252,484,-798,1232,-2002,3145,-4368,5937,-8630,
%T A363614 12112,-15504,19678,-26334,34902,-42762,51129,-65780,84337,-98336,
%U A363614 114388,-143304,175869,-201376,230120,-278256,336744,-379000,420394,-502250,598459,-658008,723065,-855042,997962,-1086008
%N A363614 Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^6.
%H A363614 Seiichi Manyama, <a href="/A363614/b363614.txt">Table of n, a(n) for n = 1..10000</a>
%F A363614 G.f.: Sum_{k>0} binomial(k+3,5) * (-x)^k/(1 - x^k).
%F A363614 a(n) = Sum_{d|n} (-1)^d * binomial(d+3,5).
%t A363614 a[n_] := DivisorSum[n, (-1)^#*Binomial[# + 3, 5] &]; Array[a, 40] (* _Amiram Eldar_, Jul 18 2023 *)
%o A363614 (PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1+x^k)^6)))
%o A363614 (PARI) a(n) = sumdiv(n, d, (-1)^d*binomial(d+3, 5));
%Y A363614 Cf. A325940, A363022, A363598, A363613.
%Y A363614 Cf. A363606.
%K A363614 sign
%O A363614 1,3
%A A363614 _Seiichi Manyama_, Jun 11 2023