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%I #12 Nov 10 2020 09:33:35
%S 0,1,6,28,170,988,7896,60492,555264,5819904,61776000,725950080,
%T 9894493440,137963243520,1875645434880,33258387456000,528975488563200,
%U 9760969019289600,175565885864140800,3608256006957772800,72367669059194880000,1745463407406243840000
%N a(n) = (n!/2) * Sum_{k=1..n-1} d(k)*d(n-k)/(k*(n-k)), where d(n) is the number of divisors of n.
%F a(n) = (n-1)! * Sum_{k=1..n-1} d(k)*d(n-k)/k.
%t a[n_] := (n - 1)! * Sum[DivisorSigma[0, k] * DivisorSigma[0, n - k]/k, {k, 1, n - 1} ]; Array[a, 22] (* _Amiram Eldar_, Nov 10 2020 *)
%o (PARI) {a(n)= n!*sum(k=1, n-1, numdiv(k)*numdiv(n-k)/(k*(n-k)))/2}
%o (PARI) {a(n)= (n-1)!*sum(k=1, n-1, numdiv(k)*numdiv(n-k)/k)}
%o (PARI) {a(n) = my(u='u); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-u/k)), n), 2)}
%Y Column 2 of A338805.
%Y Cf. A000005, A055507, A059356.
%K nonn
%O 1,3
%A _Seiichi Manyama_, Nov 10 2020
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