%I A060005
%S A060005 1,1,7,62,657,7636,93846,1199892,15796439,212681976,2915017360,
%T A060005 40536016030,570497115729,8110661588734,116307527411482,
%U A060005 1680341334827514,24435006625667338,357366669614512168
%N A060005 Number of ways of partitioning the integers {1,2,..,4n} into two (unordered) 
               sets such that the sums of parts are equal in both sets (parts in 
               either set will add up to (4n)*(4n+1)/4). Number of solutions to 
               {1 +- 2 +- 3 +- ... +- 4n=0}.
%D A060005 L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 
               90 degrees, Math. Mag. 64 (1991), 315-324.
%H A060005 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Signum equations 
               and extremal coefficients</a>.
%F A060005 a(0)=1 and a(n) is half the coefficient of q^0 in product('(q^(-k)+q^k)', 
               'k'=1..4*n) for n >= 1.
%F A060005 n>=1, a(n)=(1/Pi)*16^n*J(4n) where J(n)=integral(t=0,Pi/2,cos(t)cos(2t)...cos(nt)dt) 
               - Benoit Cloitre (abmt(AT)orange.fr), Sep 24 2006
%e A060005 a(1)=1 since there is only one way of partitioning {1,2,3,4} into two 
               sets of equal sum, namely {1,4}, {2,3}.
%Y A060005 Cf. A060468, A007219, A107350, a(n)=A058377(4n)
%Y A060005 Sequence in context: A145507 A047685 A024089 this_sequence A055066 A167550 
               A161201
%Y A060005 Adjacent sequences: A060002 A060003 A060004 this_sequence A060006 A060007 
               A060008
%K A060005 nonn
%O A060005 0,3
%A A060005 Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Mar 15 2001