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A284605 The number of partitions of n! into factorials.

%I A284605 #12 Mar 19 2020 16:01:01
%S A284605 1,1,2,5,36,1477,480733,1626159677,71503454739706,
%T A284605 49130011692806196131,616983581832732519940145403
%N A284605 The number of partitions of n! into factorials.
%F A284605 a(n) = A064986(n!).
%p A284605 A064986 := proc(n)
%p A284605     local x,d,g ;
%p A284605     g := 1;
%p A284605     for i from 1 do
%p A284605         g := g/(1-x^(i!)) ;
%p A284605         g := taylor(g,x=0,n+1) ;
%p A284605         if i! > n then
%p A284605             break ;
%p A284605         end if;
%p A284605     end do:
%p A284605     return coeftayl(%,x=0,n) ;
%p A284605 end proc:
%p A284605 for n from 0 do
%p A284605     print(n,A064986(n!)) ;
%p A284605 end do:
%t A284605 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 A284605 For[n = 0, n <= 7, n++, Print[n, " ", A064986[n!]]] (* _Jean-François Alcover_, Mar 19 2020, from Maple *)
%Y A284605 Cf. A064986.
%K A284605 nonn,more
%O A284605 0,3
%A A284605 _R. J. Mathar_, Mar 30 2017
%E A284605 a(8)-a(10) from _Alois P. Heinz_, Mar 30 2017