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%I #7 Nov 10 2020 09:33:56
%S 0,0,1,12,100,870,7588,73808,764524,8448120,103816944,1334764728,
%T 18483356736,274780501632,4371694872192,71815113008640,
%U 1282261138007040,23828058693642240,468231649812725760,9599857257164820480,205863214718290636800,4646428416182168985600
%N a(n) = (n!/6) * Sum_{i,j,k > 0 and i+j+k=n} d(i)*d(j)*d(k)/(i*j*k), where d(n) is the number of divisors of n.
%o (PARI) {a(n) = my(u='u); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-u/k)), n), 3)}
%Y Column 3 of A338805.
%Y Cf. A000005, A059357.
%K nonn
%O 1,4
%A _Seiichi Manyama_, Nov 10 2020