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a(n) = ((2*n-1)!! + (-1)^((n-1)*(n-2)/2))/2.
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%I #30 Nov 23 2017 05:13:34

%S 1,2,7,52,473,5198,67567,1013512,17229713,327364538,6874655287,

%T 158117071612,3952926790313,106729023338438,3095141676814687,

%U 95949391981255312,3166329935381425313,110821547738349885938,4100397266318945779687,159915493386438885407812

%N a(n) = ((2*n-1)!! + (-1)^((n-1)*(n-2)/2))/2.

%C Described by V. Shevelev as an instance of a fast-growing nontrivial sequence that is similar to the naturals in the sense that A007814(a(n)) = A007814(n).

%H V. Shevelev, <a href="http://arxiv.org/abs/0904.2101">Several results on sequences which are similar to the positive integers</a>, arXiv:0904.2101 [math.NT], 2009.

%o (Maxima) A220092(n):=((2*n-1)!!+(-1)^((n-1)*(n-2)/2))/2$ makelist(A220092(n),n,1,15); /* _Martin Ettl_, Dec 13 2012 */

%Y Cf. A007814.

%K nonn

%O 1,2

%A _Michel Marcus_, Dec 11 2012