A338810 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.
0, 1, 6, 28, 170, 988, 7896, 60492, 555264, 5819904, 61776000, 725950080, 9894493440, 137963243520, 1875645434880, 33258387456000, 528975488563200, 9760969019289600, 175565885864140800, 3608256006957772800, 72367669059194880000, 1745463407406243840000
Offset: 1
Keywords
Programs
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Mathematica
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 *)
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PARI
{a(n)= n!*sum(k=1, n-1, numdiv(k)*numdiv(n-k)/(k*(n-k)))/2}
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PARI
{a(n)= (n-1)!*sum(k=1, n-1, numdiv(k)*numdiv(n-k)/k)}
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PARI
{a(n) = my(u='u); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-u/k)), n), 2)}
Formula
a(n) = (n-1)! * Sum_{k=1..n-1} d(k)*d(n-k)/k.