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A066998 a(0)=0; a(n) = n^2*a(n-1) + 1. 1

%I

%S 0,1,5,46,737,18426,663337,32503514,2080224897,168498216658,

%T 16849821665801,2038828421561922,293591292704916769,

%U 49616928467130933962,9724917979557663056553,2188106545400474187724426

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

%C if s(n) is a sequence defined as s(0)=x, s(n) = n^2*s(n-1) + k, then s(n) = n!^2*x + a(n)*k. - _Gary Detlefs_, Feb 20 2010

%H Harry J. Smith, <a href="/A066998/b066998.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = (n!)^2*Sum_{i=1..n} 1/(i!)^2.

%F a(n) = floor((1-BesselI(0, 2))*(n!)^2). - _Benoit Cloitre_, Nov 02 2002

%t RecurrenceTable[{a[0]==0,a[n]==n^2 a[n-1]+1},a,{n,20}] (* _Harvey P. Dale_, Jan 24 2019 *)

%o (PARI) { for (n=0, 100, if (n==0, a=0, a=n^2*a + 1); write("b066998.txt", n, " ", a) ) } \\ _Harry J. Smith_, Apr 24 2010

%Y This is the same recurrence relation as A006040 except A006040 has a(0) = 1.

%K nonn

%O 0,3

%A _Benoit Cloitre_, Jan 27 2002

%E Better description from _James D. Klein_, Feb 25 2002

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Last modified September 27 09:09 EDT 2020. Contains 337380 sequences. (Running on oeis4.)