%I A047653
%S A047653 1,2,4,10,26,76,236,760,2522,8556,29504,103130,364548,1300820,4679472,
%T A047653 16952162,61790442,226451036,833918840,3084255128,11451630044,
%U A047653 42669225172,159497648600,597950875256,2247724108772,8470205600640
%N A047653 Constant term in expansion of (1/2) * Prod_{k=-n..n} 1+x^k.
%C A047653 Or, constant term in expansion of Prod_{k=1..n} (x^k+1/x^k)^2. - N. J. 
               A. Sloane (njas(AT)research.att.com), Jul 09 2008
%C A047653 Or, maximal coefficient of the polynomial (1+x)^2 * (1+x^2)^2 *...* (1+x^n)^2.
%D A047653 R. P. Stanley, Weyl groups, the hard Lefschetz theorem and the Sperner 
               property, SIAM J. Algebraic and Discrete Methods 1 (1980), 168-184.
%H A047653 T. D. Noe, <a href="b047653.txt">Table of n, a(n) for n=0..200</a>
%H A047653 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Signum equations 
               and extremal coefficients</a>.
%p A047653 f:=n->coeff( expand( mul((x^k+1/x^k)^2,k=1..n) ),x,0);
%o A047653 (PARI) a(n)=polcoeff(prod(k=-n,n,1+x^k),0)/2
%Y A047653 a(n)=A000980(n)/2. Cf. A025591.
%Y A047653 Sequence in context: A007578 A007580 A000085 this_sequence A148100 A149815 
               A149816
%Y A047653 Adjacent sequences: A047650 A047651 A047652 this_sequence A047654 A047655 
               A047656
%K A047653 nonn
%O A047653 0,2
%A A047653 N. J. A. Sloane (njas(AT)research.att.com).
%E A047653 More terms from Michael Somos, Jun 10, 2000.