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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. 1
0, 1, 6, 28, 170, 988, 7896, 60492, 555264, 5819904, 61776000, 725950080, 9894493440, 137963243520, 1875645434880, 33258387456000, 528975488563200, 9760969019289600, 175565885864140800, 3608256006957772800, 72367669059194880000, 1745463407406243840000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 22:39 EDT 2022. Contains 354110 sequences. (Running on oeis4.)