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%I #9 Sep 20 2024 06:07:21
%S 0,1,14,83,324,986,2484,5625,11304,21596,37824,64746,103252,163536,
%T 244200,364855,517478,741087,1009244,1394080,1842690,2470668,3178188,
%U 4171260,5242610,6735966,8331338,10511692,12777898,15922212,19067506,23429969,27785000,33707290
%N a(n) = Sum_{k=1..n-1} sigma_2(k) * sigma_3(n-k).
%C In general, if k>=1, m>=1 and a(n) = Sum_{j=1..n-1} sigma_k(j) * sigma_m(n-j), then Sum_{j=1..n} a(j) ~ Gamma(k+1) * Gamma(m+1) * zeta(k+1) * zeta(m+1) * n^(k+m+2) / Gamma(k+m+3).
%F Sum_{k=1..n} a(k) ~ Pi^4 * zeta(3) * n^7 / 37800.
%t Table[Sum[DivisorSigma[2, k]*DivisorSigma[3, n-k], {k, n-1}], {n, 1, 50}]
%o (PARI) a(n) = sum(k=1, n-1, sigma(k, 2) * sigma(n-k, 3)); \\ _Michel Marcus_, Sep 19 2024
%Y Cf. A001157, A001158, A374974, A374963.
%K nonn
%O 1,3
%A _Vaclav Kotesovec_, Sep 19 2024