A217284 a(n) = Sum_{k=0..n} (n!/k!)^3.

1, 2, 17, 460, 29441, 3680126, 794907217, 272653175432, 139598425821185, 101767252423643866, 101767252423643866001, 135452212975869985647332, 234061424022303335198589697, 514232948577000427431301564310, 1411055210895289172871491492466641, 4762311336771600958441283787074913376

Offset: 0

Author

Vaclav Kotesovec, Sep 30 2012

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..180

Crossrefs

Cf. A000522, A006040, A271574, A336247.

Programs

Mathematica

Table[Sum[(n!/k!)^3, {k, 0, n}], {n, 0, 20}]

PARI

a(n) = sum(k=0, n, (n!/k!)^3); \\ Seiichi Manyama, May 02 2021

Formula

Recurrence: a(n) = (n+1)*(n^2-n+1)*a(n-1)-(n-1)^3*a(n-2).

a(n) ~ 2.12970254898330641813452361... * (n!)^3 = A271574 * (n!)^3.

a(n) = n^3 * a(n-1) + 1. - Seiichi Manyama, May 02 2021