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%I #69 Nov 15 2022 01:18:03
%S 0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,
%T -20,-21,-22,-23,-24,-25,-26,-27,-28,-29,-30,-31,-32,-33,-34,-35,-36,
%U -37,-38,-39,-40,-41,-42,-43,-44,-45,-46,-47,-48,-49,-50,-51,-52,-53,-54,-55,-56,-57,-58,-59,-60,-61,-62,-63,-64,-65
%N a(n) = -n.
%C Also: the nonpositive integers, listed with offset = 0 and in decreasing order.
%C An involution: the function is its own inverse, A001489 o A001489 = A001477, the identity function on N = {0, 1, 2, 3, ...}. - _M. F. Hasler_, Jan 18 2015
%H David Wasserman, <a href="/A001489/b001489.txt">Table of n, a(n) for n = 0..1000</a>
%H D. Dumont and J. Zeng, <a href="http://dx.doi.org/10.1023/A:1009759202242">Polynomes d'Euler et les fractions continues de Stieltjes-Rogers</a>, Ramanujan J. 2 (1998) 3, 387-410.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A. Randrianarivony and J. Zeng, <a href="http://dx.doi.org/10.1006/aama.1996.0001">Une famille de polynomes qui interpole plusieurs suites classiques de nombres</a>, Adv. Appl. Math. 17 (1996), 1-26.
%H J. Zeng, <a href="http://dx.doi.org/10.1016/0012-365X(95)00145-M">Sur quelques propriétés de symétrie des nombres de Genocchi</a>, Discr. Math. 153 (1996) 319-333.
%H <a href="/index/Cor#core">Index entries for "core" sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = -n.
%F G.f.: -x/(1-x)^2.
%F a(n) = -a(-n) for all n in Z. - _Michael Somos_, Aug 04 2018
%e G.f. = -x - 2*x^2 - 3*x^3 - 4*x^4 - 5*x^5 - 6*x^6 - 7*x^7 - ... - _Michael Somos_, Aug 04 2018
%p A001489 := n->-n;
%p [ seq(-n,n=0..100) ];
%t Table[ -n, {n, 0, 50}] (* _Stefan Steinerberger_, Apr 01 2006 *)
%o (PARI) a(n)=-n \\ _Charles R Greathouse IV_, Jun 04 2013
%o (Python)
%o def A001489(n): return -n # _Chai Wah Wu_, Nov 14 2022
%Y Partial sums of A057428.
%K core,sign,easy
%O 0,3
%A _N. J. A. Sloane_
%E Edited by _M. F. Hasler_, Jan 18 2015
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