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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..10.

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-Fran├žois Alcover, Mar 19 2020, from Maple *)

CROSSREFS

Cf. A064986.

Sequence in context: A317801 A111491 A331402 * A106129 A163499 A086218

Adjacent sequences:  A284602 A284603 A284604 * A284606 A284607 A284608

KEYWORD

nonn,more

AUTHOR

R. J. Mathar, Mar 30 2017

EXTENSIONS

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

STATUS

approved

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Last modified April 18 13:46 EDT 2021. Contains 343088 sequences. (Running on oeis4.)