%I A123237
%S A123237 1,1,12,144,2400,28224,1296000,50808384,2434614000,85975622656,8396400230400,
%T A123237 691198592910336,65694715632000000,4784543769600000000,796566295447796966400,
%U A123237 112616674749446400000000,17805426854398997299200000,2223594618178251399873232896
%V A123237 1,-1,-12,144,2400,-28224,-1296000,50808384,2434614000,-85975622656,-8396400230400,
%W A123237 691198592910336,65694715632000000,-4784543769600000000,-796566295447796966400,
%X A123237 112616674749446400000000,17805426854398997299200000,-2223594618178251399873232896
%N A123237 A000316-like neo-Hankel matrix determinant sequence.
%C A123237 This neo-Hankel matrix type is symmetrical about the diagonal: The average 
               (i*(j+1)/2+j*(i+1)/2)/4 =(i+j+2*i*j)/4 term is based on the sum of 
               integers n(n+1)/2. I get Log plot fit of an exponent: Det[M[n]]=c*n^4.2586 
               a0 = Table[Det[Table[ If[i + j - 1 > m, 0, Floor[(i + j + 2*i*j)/
               4]], {i, 1, m}, {j, 1, m}]], {m, 3, 20}]; a = N[Log[Abs[%]]]; g1 
               = ListPlot[a, PlotJoined -> True]; y[x_] = Fit[a, {1, x}, x] g2 = 
               Plot[y[x], {x, 0, 20}]; Show[{g1, g2}]
%F A123237 mij=If[i + j - 1 > m, 0, Floor[(i + j + 2*i*j)/4]]
%t A123237 Table[Det[Table[If[i + j - 1 > m, 0, Floor[(i + j + 2*i*j)/4]], {i, 1, 
               m}, {j, 1, m}]], {m, 1, 20}]
%Y A123237 Cf. A000316.
%Y A123237 Sequence in context: A159490 A000468 A076728 this_sequence A143248 A138444 
               A137886
%Y A123237 Adjacent sequences: A123234 A123235 A123236 this_sequence A123238 A123239 
               A123240
%K A123237 uned,sign
%O A123237 1,3
%A A123237 Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 06 2006