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 A374977 #27 Jul 11 2025 15:37:10
%S A374977 0,0,0,1,12,70,280,885,2364,5586,12000,23870,44660,79272,134768,
%T A374977 220565,349440,538270,807840,1187004,1706840,2415150,3354120,4601870,
%U A374977 6209612,8303610,10935960,14309640,18460260,23708184,30044000,37967925,47368480,59022432,72633816
%N A374977 a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 1} sigma(i)*sigma(j)*sigma(k)*sigma(l).
%H A374977 Vaclav Kotesovec, <a href="/A374977/b374977.txt">Table of n, a(n) for n = 1..10000</a>
%F A374977 4-fold convolution of A000203.
%F A374977 Convolution of A000203 and A374951.
%F A374977 Convolution of A000385 with itself.
%F A374977 a(n) = Sum_{i=1..n-1} A000203(i)*A374951(n-i).
%F A374977 a(n) = Sum_{i=1..n-3} A000385(i)*A000385(n-i-2).
%F A374977 Column k=4 of A319083.
%F A374977 Sum_{k=1..n} a(k) ~ Pi^8 * n^8 / 52254720. - _Vaclav Kotesovec_, Sep 20 2024
%t A374977 b[n_, k_] := b[n, k] = If[k == 0, If[n == 0, 1, 0], If[k == 1, If[n == 0, 0, DivisorSigma[1, n]], Function[q, Sum[b[j, q]*b[n - j, k - q], {j, 0, n}]][Quotient[k, 2]]]];
%t A374977 a[n_] := b[n, 4];
%t A374977 Table[a[n], {n, 1, 35}] (* _Jean-François Alcover_, Jul 11 2025, after _Alois P. Heinz_ in A319083 *)
%o A374977 (Python)
%o A374977 from sympy import divisor_sigma
%o A374977 def A374977(n): return sum((5*divisor_sigma(i+1,3)-(5+6*i)*divisor_sigma(i+1))*(5*divisor_sigma(n-i-1,3)-(5+6*(n-i-2))*divisor_sigma(n-i-1)) for i in range(1,n-2))//144
%Y A374977 Cf. A000203, A000385, A319083, A374951.
%K A374977 nonn
%O A374977 1,5
%A A374977 _Chai Wah Wu_, Jul 26 2024