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 A374973 #14 Jul 26 2024 10:21:14 %S A374973 0,1,7,22,54,105,188,307,459,690,937,1307,1680,2260,2740,3588,4221, %T A374973 5402,6163,7714,8694,10723,11758,14449,15574,18884,20320,24228,25626, %U A374973 30768,32038,37985,39826,46515,47898,56877,57754,67433,69450,80062,81103,95034,94941 %N A374973 a(n) = Sum_{k=1..n-1} tau(k) * sigma_2(n-k). %C A374973 Convolution of tau with sigma_2. %F A374973 G.f.: ( Sum_{k>=1} x^k/(1 - x^k) ) * ( Sum_{k>=1} k^2 * x^k/(1 - x^k) ). %o A374973 (PARI) a(n) = sum(k=1, n-1, sigma(k, 0)*sigma(n-k, 2)); %o A374973 (PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^k/(1-x^k))*sum(k=1, N, k^2*x^k/(1-x^k)))) %Y A374973 Cf. A000005, A001157, A055507, A191831. %K A374973 nonn,easy %O A374973 1,3 %A A374973 _Seiichi Manyama_, Jul 26 2024