A284605 The number of partitions of n! into factorials.

1, 1, 2, 5, 36, 1477, 480733, 1626159677, 71503454739706, 49130011692806196131, 616983581832732519940145403, 162270066262338926770105014493754479, 1007976978268717217370514961374572506826114126, 164671704320997843373466981852528064894015042582119533651

Offset

0,3

Links

Martin Fuller, Table of n, a(n) for n = 0..20

Martin Fuller, PARI program

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 *)

Prog

(PARI) /* See Fuller link */

Crossrefs

Cf. A064986.

Sequence in context: A317801 A111491 A331402 * A106129 A163499 A086218

Adjacent sequences: A284602 A284603 A284604 * A284606 A284607 A284608

Keyword

nonn

Author

R. J. Mathar, Mar 30 2017

Extensions

a(8)-a(10) from Alois P. Heinz, Mar 30 2017

a(11) onward from Martin Fuller, Jan 19 2026

Status

approved