A284603 The number of partitions of n! into divisors of n!.

1, 1, 2, 8, 458, 21802430, 1649163472071932218, 1653665874514973907764084044114212937546257191, 19380136043740051359260580553911591207343629434762856702614857704914203110061632119814747632404

Offset

0,3

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = A018818(n!).

Maple

A018818 := proc(n)
    local x, d, g ;
    g := 1;
    for d in numtheory[divisors](n) do
        g := g/(1-x^d) ;
        g := taylor(g, x=0, n+1) ;
    end do:
    return coeftayl(%, x=0, n) ;
end proc:
for n from 0 to 10 do
    print(n, A018818(n!)) ;
end do:

Mathematica

b[n_] := SeriesCoefficient[1/Product[1 - x^d, {d, Divisors[n]}], {x, 0, n}];
a[n_] := b[n!];
a /@ Range[0, 7] (* Jean-François Alcover, Nov 29 2020 *)

Crossrefs

Cf. A018818.

Sequence in context: A367998 A009808 A035129 * A329685 A323863 A003301

Adjacent sequences: A284600 A284601 A284602 * A284604 A284605 A284606

Keyword

nonn

Author

R. J. Mathar, Mar 30 2017

Extensions

a(8) from Alois P. Heinz, Mar 30 2017

Status

approved