A284603 - OEIS

A284603

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

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

(list; graph; refs; listen; history; text; internal format)

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