0,4

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

Zivkovic (Math. Comp. 68 (1999), pp. 403-409).

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.

Index entries for sequences related to factorial numbers

Eric Weisstein's World of Mathematics, Alternating Factorial

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

A005165 := proc(n) local i; add((-1)^(n-i)*i!, i=1..n); end;

(PARI) a(n)=if(n<0, 0, sum(k=0, n-1, (-1)^k*(n-k)!))

Cf. A000142, A003422, A071828, A001272.

Sequence in context: A106958 A146144 A162292 this_sequence A071828 A158615 A088180

Adjacent sequences: A005162 A005163 A005164 this_sequence A005166 A005167 A005168

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).