Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Sep 20 2024 05:33:51
%S 0,0,0,1,12,70,280,885,2364,5586,12000,23870,44660,79272,134768,
%T 220565,349440,538270,807840,1187004,1706840,2415150,3354120,4601870,
%U 6209612,8303610,10935960,14309640,18460260,23708184,30044000,37967925,47368480,59022432,72633816
%N a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 1} sigma(i)*sigma(j)*sigma(k)*sigma(l).
%H Vaclav Kotesovec, <a href="/A374977/b374977.txt">Table of n, a(n) for n = 1..10000</a>
%F 4-fold convolution of A000203.
%F Convolution of A000203 and A374951.
%F Convolution of A000385 with itself.
%F a(n) = Sum_{i=1..n-1} A000203(i)*A374951(n-i).
%F a(n) = Sum_{i=1..n-3} A000385(i)*A000385(n-i-2).
%F Column k=4 of A319083.
%F Sum_{k=1..n} a(k) ~ Pi^8 * n^8 / 52254720. - _Vaclav Kotesovec_, Sep 20 2024
%o (Python)
%o from sympy import divisor_sigma
%o 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 Cf. A000203, A000385, A319083, A374951.
%K nonn
%O 1,5
%A _Chai Wah Wu_, Jul 26 2024