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

1,3

Links

Table of n, a(n) for n=1..22.

Formula

a(n) = (n-1)! * Sum_{k=1..n-1} d(k)*d(n-k)/k.

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 *)

Prog

(PARI) {a(n)= n!*sum(k=1, n-1, numdiv(k)*numdiv(n-k)/(k*(n-k)))/2}
(PARI) {a(n)= (n-1)!*sum(k=1, n-1, numdiv(k)*numdiv(n-k)/k)}
(PARI) {a(n) = my(u='u); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-u/k)), n), 2)}

Crossrefs

Column 2 of A338805.

Cf. A000005, A055507, A059356.

Sequence in context: A047129 A173081 A278015 * A345002 A169723 A052395

Adjacent sequences: A338807 A338808 A338809 * A338811 A338812 A338813

Keyword

nonn

Author

Seiichi Manyama, Nov 10 2020

Status

approved