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The number of partitions of n! into divisors of n!.
0

%I #13 Nov 29 2020 02:11:16

%S 1,1,2,8,458,21802430,1649163472071932218,

%T 1653665874514973907764084044114212937546257191,

%U 19380136043740051359260580553911591207343629434762856702614857704914203110061632119814747632404

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

%F a(n) = A018818(n!).

%p A018818 := proc(n)

%p local x,d,g ;

%p g := 1;

%p for d in numtheory[divisors](n) do

%p g := g/(1-x^d) ;

%p g := taylor(g,x=0,n+1) ;

%p end do:

%p return coeftayl(%,x=0,n) ;

%p end proc:

%p for n from 0 to 10 do

%p print(n,A018818(n!)) ;

%p end do:

%t b[n_] := SeriesCoefficient[1/Product[1 - x^d, {d, Divisors[n]}], {x, 0, n}];

%t a[n_] := b[n!];

%t a /@ Range[0, 7] (* _Jean-François Alcover_, Nov 29 2020 *)

%Y Cf. A018818.

%K nonn

%O 0,3

%A _R. J. Mathar_, Mar 30 2017

%E a(8) from _Alois P. Heinz_, Mar 30 2017