Search: id:A137501
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%I A137501
%S A137501 0,0,2,2,4,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20,20,22,22,24,24,26,
%T A137501 26,28,28,30,30,32,32,34,34,36,36,38,38,40,40,42,42,44,44,46,46,48,48,
               50,
%U A137501 50,52,52,54,54,56,56,58,58,60,60,62,62,64,64,66,66,68,68,70,70,72,72,
               74
%V A137501 0,0,2,-2,4,-4,6,-6,8,-8,10,-10,12,-12,14,-14,16,-16,18,-18,20,-20,22,
               -22,24,-24,26,
%W A137501 -26,28,-28,30,-30,32,-32,34,-34,36,-36,38,-38,40,-40,42,-42,44,-44,46,
               -46,48,-48,50,
%X A137501 -50,52,-52,54,-54,56,-56,58,-58,60,-60,62,-62,64,-64,66,-66,68,-68,70,
               -70,72,-72,74
%N A137501 The even numbers repeated and with the sign changed.
%C A137501 Contribution from Peter Luschny (peter(AT)luschny.de), Jul 12 2009: (Start)
%C A137501 The general formula for alternating sums of powers of even integers is 
               in terms of the Swiss-Knife polynomials P(n,x) A153641 (P(n,1)-(-1)^k 
               P(n,2k+1))/2. Here n=1 and k shifted one place, thus
%C A137501 a(k) = (P(1,1)-(-1)^(k-1) P(1,2(k-1)+1))/2. (End)
%F A137501 a(n) = ( n - (1/2) + (1/2)*(-1)^n )*(-1)^n
%p A137501 den:= n -> (n-1/2+1/2*(-1)^n)*(-1)^n: seq(den(n),n=-10..10);
%p A137501 a := n -> (1+(-1)^n*(2*n-1))/2; [From Peter Luschny (peter(AT)luschny.de), 
               Jul 12 2009]
%Y A137501 Cf. A052928.
%Y A137501 Sequence in context: A161764 A131055 A052928 this_sequence A005186 A008642 
               A001364
%Y A137501 Adjacent sequences: A137498 A137499 A137500 this_sequence A137502 A137503 
               A137504
%K A137501 easy,sign
%O A137501 0,3
%A A137501 Carlos Alberto da Costa Filho (cacau_dacosta(AT)hotmail.com), Apr 22 
               2008

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