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a(n) = (-1)^[(n+1)/2] A000108([n/2]+1).
5

%I #7 Aug 25 2012 16:41:18

%S 1,-1,-2,2,5,-5,-14,14,42,-42,-132,132,429,-429,-1430,1430,4862,-4862,

%T -16796,16796,58786,-58786,-208012,208012,742900,-742900,-2674440,

%U 2674440,9694845,-9694845,-35357670,35357670,129644790,-129644790,-477638700,477638700

%N a(n) = (-1)^[(n+1)/2] A000108([n/2]+1).

%C Terms of A000108(1,...) repeated, changing sign between the two repeated terms of same magnitude, but keeping the same sign for the next (larger) term. - _M. F. Hasler_, Aug 25 2012

%F First differences of A129110: a(n)=A129110(n+1)-A129110(n).

%o (PARI) A129996(n)=(-1)^((n+1)\2)*A000108(n\2+1) \\ - _M. F. Hasler_, Aug 25 2012

%Y Cf. A099363, A106181 and A208355, which also consist of duplicated terms of A000108. - _M. F. Hasler_, Aug 25 2012

%K sign

%O 0,3

%A _Paul Curtz_, Jun 15 2007

%E Definition (formula) corrected by _M. F. Hasler_, Aug 25 2012