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A005165
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Alternating factorials: n! - (n-1)! + (n-2)! - ... 1!.
(Formerly M3892)
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10
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0, 1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, 1226280710981, 19696509177019, 335990918918981, 6066382786809019, 115578717622022981, 2317323290554617019, 48773618881154822981
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Conjecture: for n > 2, smallest prime divisor of a(n) > n. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jun 19 2004. Rebuttal: This is not true - Zivkovic (Math. Comp. 68 (1999), pp. 403-409) has demonstrated that 3612703 divides A_{n} for all n >= 3612702. - Paul Jobling, Oct 18 2004.
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REFERENCES
| R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.
R. K. Guy, Unsolved Problems in Number Theory, B43.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Zivkovic (Math. Comp. 68 (1999), pp. 403-409).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
E. Wegrzynowski, Series de factorielles
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Alternating Factorial
Index entries for sequences related to factorial numbers
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FORMULA
| a(0) = 0, a(n) = n! - a(n-1) for n > 0 also a(n) = n*a(n-2) + (n-1)*a(n-1) for n > 1. Sum n=1..inf PI^n/a(n) ~ 30.00005. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jun 19 2004
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MAPLE
| A005165 := proc(n) local i; add((-1)^(n-i)*i!, i=1..n); end;
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MATHEMATICA
| nn=25; With[{fctrls=Range[nn]!}, Table[Abs[Total[Times@@@Partition[ Riffle[ Take[ fctrls, n], {1, -1}], 2]]], {n, nn}]] (* From Harvey P. Dale, Dec 10 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, sum(k=0, n-1, (-1)^k*(n-k)!))
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CROSSREFS
| Cf. A000142, A003422, A071828, A001272.
Sequence in context: A106958 A146144 A162292 * A071828 A158615 A088180
Adjacent sequences: A005162 A005163 A005164 * A005166 A005167 A005168
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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