A193563 - OEIS

%I #21 Jan 05 2024 07:57:22

%S 0,1,8,81,1312,32825,1181736,57905113,3705927296,300180111057,

%T 30018011105800,3632179343801921,523033825507476768,

%U 88392716510763573961,17324972436109660496552,3898118798124673611724425,997918412319916444601453056

%N a(0) = 0, a(n) = n^2 * (a(n-1) + 1).

%F From _Seiichi Manyama_, Jan 05 2024: (Start)

%F a(n) = (n!)^2 * Sum_{k=0..n} (k/k!)^2.

%F a(n) = n^2 * A006040(n-1) for n > 0. (End)

%p seq(n!^2*add(1/k!^2,k=0..n-1),n=0..16);   # _Mark van Hoeij_, May 13 2013

%o (PARI) a=[0];for(n=1,20,a=concat(a,(a[#a]+1)*n^2));a \\ _Charles R Greathouse IV_, Jul 31 2011

%Y Cf. A006040, A007526 (multiply by n instead of n^2), A180255.

%K nonn,easy

%O 0,3

%A _Meherzad Lahewala_, Jul 31 2011