A284605 - OEIS

%I #12 Mar 19 2020 16:01:01

%S 1,1,2,5,36,1477,480733,1626159677,71503454739706,

%T 49130011692806196131,616983581832732519940145403

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

%F a(n) = A064986(n!).

%p A064986 := proc(n)

%p     local x,d,g ;

%p     g := 1;

%p     for i from 1 do

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

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

%p         if i! > n then

%p             break ;

%p         end if;

%p     end do:

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

%p end proc:

%p for n from 0 do

%p     print(n,A064986(n!)) ;

%p end do:

%t A064986[n_] := Module[{x, d, g = 1}, For[i = 1, True, i++, g = g/(1 - x^(i!)); g = Series[g, {x, 0, n+1}]; If[i! > n, Break[]]]; Return[ SeriesCoefficient[g, {x, 0, n}]]];

%t For[n = 0, n <= 7, n++, Print[n, " ", A064986[n!]]] (* _Jean-François Alcover_, Mar 19 2020, from Maple *)

%Y Cf. A064986.

%K nonn,more

%O 0,3

%A _R. J. Mathar_, Mar 30 2017

%E a(8)-a(10) from _Alois P. Heinz_, Mar 30 2017