A217284 - OEIS

%I #19 Jan 05 2024 06:43:35

%S 1,2,17,460,29441,3680126,794907217,272653175432,139598425821185,

%T 101767252423643866,101767252423643866001,135452212975869985647332,

%U 234061424022303335198589697,514232948577000427431301564310,1411055210895289172871491492466641,4762311336771600958441283787074913376

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

%H Vincenzo Librandi, <a href="/A217284/b217284.txt">Table of n, a(n) for n = 0..180</a>

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

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

%F a(n) = n^3 * a(n-1) + 1. - _Seiichi Manyama_, May 02 2021

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

%o (PARI) a(n) = sum(k=0, n, (n!/k!)^3); \\ _Seiichi Manyama_, May 02 2021

%Y Cf. A000522, A006040, A271574, A336247.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Sep 30 2012