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 A356039 #14 Feb 16 2025 08:34:03
%S A356039 1,11,58,243,866,2804,8485,24387,67333,180086,469338,1196976,2996956,
%T A356039 7385837,17954243,43125267,102494548,241309031,563341508,1305142418,
%U A356039 3002938045,6866090880,15609292379,35299794600,79443050541,177989130174,397124963671,882642816697,1954708794400
%N A356039 a(n) = Sum_{k=1..n} binomial(n,k) * sigma_3(k).
%C A356039 For m>0, Sum_{k=1..n} binomial(n,k) * sigma_m(k) ~ zeta(m+1) * n^m * 2^(n-m).
%H A356039 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>.
%F A356039 a(n) ~ Pi^4 * n^3 * 2^(n-4) / 45.
%F A356039 a(n) = Sum_{i=1..n} Sum_{j=1..n} (i^3)*binomial(n,i*j). - _Ridouane Oudra_, Oct 31 2022
%p A356039 with(numtheory): seq(add(sigma[3](i)*binomial(n,i), i=1..n), n=1..60); # _Ridouane Oudra_, Oct 31 2022
%t A356039 Table[Sum[Binomial[n, k] * DivisorSigma[3, k], {k, 1, n}], {n, 1, 40}]
%o A356039 (PARI) a(n) = sum(k=1, n, binomial(n,k) * sigma(k, 3)); \\ _Michel Marcus_, Jul 24 2022
%Y A356039 Cf. A001158, A160399, A185003, A356038.
%Y A356039 Cf. A006218, A024916, A064602, A064603.
%K A356039 nonn
%O A356039 1,2
%A A356039 _Vaclav Kotesovec_, Jul 24 2022