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 A386781 #21 Aug 04 2025 06:15:26
%S A386781 0,1,1032,59076,1056832,9765750,60966432,282475592,1082196480,
%T A386781 3488379453,10078254000,25937425932,62433407232,137858494046,
%U A386781 291514810944,576921447000,1108169199616,2015993905362,3600007595496,6131066264660,10320757104000,16687528072992,26767423561824
%N A386781 a(n) = n^3*sigma_7(n).
%H A386781 Vincenzo Librandi, <a href="/A386781/b386781.txt">Table of n, a(n) for n = 0..10000</a>
%F A386781 G.f.: Sum_{k>=1} k^10*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4.
%F A386781 a(n) = (3*A386813(n) + 5*A282549(n) - 9*A282792(n) - 3*A058550(n) + 4*A282576(n))/3456.
%F A386781 a(n) = n^3*A013955(n).
%F A386781 Dirichlet g.f.: zeta(s-3)*zeta(s-10). - _R. J. Mathar_, Aug 03 2025
%t A386781 Table[n^3*DivisorSigma[7, n], {n, 0, 30}]
%t A386781 (* or *)
%t A386781 nmax = 30; CoefficientList[Series[Sum[k^10*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]
%t A386781 (* or *)
%t A386781 terms = 30; E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}]; E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}]; E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}]; CoefficientList[Series[(3*E2[x]^3*E4[x]^2 + 5*E2[x]*E4[x]^3 - 9*E2[x]^2*E4[x]*E6[x] - 3*E4[x]^2*E6[x] + 4*E2[x]*E6[x]^2)/3456, {x, 0, terms}], x]
%o A386781 (Magma) [0] cat [n^3*DivisorSigma(7, n): n in [1..35]]; // _Vincenzo Librandi_, Aug 04 2025
%Y A386781 Cf. A282211, A386746, A282213, A386748, A282781, A386780, A386782.
%Y A386781 Cf. A013955, A282060, A282753.
%Y A386781 Cf. A386813, A282549, A282792, A058550, A282576.
%K A386781 nonn,mult
%O A386781 0,3
%A A386781 _Vaclav Kotesovec_, Aug 02 2025