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%I #2 Mar 30 2012 17:34:36
%S 1,1,3,2,3,7,17,17,7,15,116,122,116,15,31,627,1262,1262,627,31,63,
%T 2990,12433,15108,12433,2990,63,127,13309,107151,201973,201973,107151,
%U 13309,127,255,56936,830628,2612184,3321914,2612184,830628,56936,255,511
%N Coefficient expansion of: f(t,y)=((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t])
%C Row sums are:
%C 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200,...
%F f(t,y)=((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t])
%e {1, 1},
%e {3, 2, 3},
%e {7, 17, 17, 7},
%e {15, 116, 122, 116, 15},
%e {31, 627, 1262, 1262, 627, 31}, {63, 2990, 12433, 15108, 12433, 2990, 63},
%e {127, 13309, 107151, 201973, 201973, 107151, 13309, 127},
%e {255, 56936, 830628, 2612184, 3321914, 2612184, 830628, 56936, 255},
%e {511, 237863, 5979980, 30947132, 55731794, 55731794, 30947132, 5979980, 237863, 511},
%e {1023, 979298, 40909331, 336803864, 900995822, 1156512524, 900995822, 336803864, 40909331, 979298, 1023}
%t f[t_, y_] = ((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t]);
%t a = Table[ CoefficientList[FullSimplify[ExpandAll[(-1 + y)^(n + 1)*(-2)^n*n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 1, 10}]
%t Flatten[a]
%K nonn,uned
%O 1,3
%A _Roger L. Bagula_, Dec 16 2009
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