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Coefficient expansion of: f(t,y)=((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t])
0

%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