%I A109771
%S A109771 1,3,4,12,44,180,788,3612,17116,83172,412196,2075436,10586892,54595476,
%T A109771 284157492,1490774076,7875206076,41854313412,223636052036,1200637707852,
%U A109771 6473448634348,35037238641780,190299310403924,1036863750837852,5665846701859484
%V A109771 1,3,-4,12,-44,180,-788,3612,-17116,83172,-412196,2075436,-10586892,54595476,
%W A109771 -284157492,1490774076,-7875206076,41854313412,-223636052036,1200637707852,
%X A109771 -6473448634348,35037238641780,-190299310403924,1036863750837852,-5665846701859484
%N A109771 G.f.: sqrt(1+6*x+x^2).
%C A109771 G.f. = square root of weight enumerator of [4,3,2] even weight code.
%C A109771 a(n) gives the row sums of the coefficient array for the family Gegenbauer_C(n,
               -1/2,-2x-1). [From Paul Barry (pbarry(AT)wit.ie), Apr 20 2009]
%H A109771 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/
               abs/math.NT/0509316">On the Integrality of n-th Roots of Generating 
               Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%F A109771 a(n)=(-1)^n*sum{k=0..n, C(n+k-2,n-k)*C(2k,k)/(1-2k)}=(-1)^n*sum{k=0..n, 
               C(n+k-2,n-k)*A002420(k)}; [From Paul Barry (pbarry(AT)wit.ie), Apr 
               20 2009]
%e A109771 1+3*x-4*x^2+12*x^3-44*x^4+180*x^5-788*x^6+3612*x^7-...
%Y A109771 Sequence in context: A000208 A079154 A101716 this_sequence A052626 A122903 
               A059792
%Y A109771 Adjacent sequences: A109768 A109769 A109770 this_sequence A109772 A109773 
               A109774
%K A109771 sign
%O A109771 0,2
%A A109771 N. J. A. Sloane (njas(AT)research.att.com) and Nadia Heninger (nadiah(AT)cs.princeton.edu), 
               Aug 13 2005