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A284605
The number of partitions of n! into factorials.
11
1, 1, 2, 5, 36, 1477, 480733, 1626159677, 71503454739706, 49130011692806196131, 616983581832732519940145403
OFFSET
0,3
FORMULA
a(n) = A064986(n!).
MAPLE
A064986 := proc(n)
local x, d, g ;
g := 1;
for i from 1 do
g := g/(1-x^(i!)) ;
g := taylor(g, x=0, n+1) ;
if i! > n then
break ;
end if;
end do:
return coeftayl(%, x=0, n) ;
end proc:
for n from 0 do
print(n, A064986(n!)) ;
end do:
MATHEMATICA
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}]]];
For[n = 0, n <= 7, n++, Print[n, " ", A064986[n!]]] (* Jean-François Alcover, Mar 19 2020, from Maple *)
CROSSREFS
Cf. A064986.
Sequence in context: A317801 A111491 A331402 * A106129 A163499 A086218
KEYWORD
nonn,more
AUTHOR
R. J. Mathar, Mar 30 2017
EXTENSIONS
a(8)-a(10) from Alois P. Heinz, Mar 30 2017
STATUS
approved