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A066998 a(0)=0; a(n) = n^2*a(n-1) + 1. 1
0, 1, 5, 46, 737, 18426, 663337, 32503514, 2080224897, 168498216658, 16849821665801, 2038828421561922, 293591292704916769, 49616928467130933962, 9724917979557663056553, 2188106545400474187724426 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..100

FORMULA

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

a(n) = floor((1-BesselI(0, 2))*(n!)^2). - Benoit Cloitre, Nov 02 2002

PROG

(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

CROSSREFS

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

Sequence in context: A052894 A292408 A295552 * A036246 A183240 A299715

Adjacent sequences:  A066995 A066996 A066997 * A066999 A067000 A067001

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 27 2002

EXTENSIONS

Better description from James D. Klein, Feb 25 2002

STATUS

approved

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Last modified January 18 11:28 EST 2019. Contains 319271 sequences. (Running on oeis4.)