A168347 - OEIS

%I #2 Mar 30 2012 17:34:35

%S 1,1,2,1,1,7,7,9,1,18,39,68,55,10,1,1,41,181,381,691,395,215,15,1,88,

%T 733,2048,5378,6512,5026,2816,381,56,1,1,183,2703,10921,34826,71590,

%U 78590,76146,34853,11123,1603,21,1,374,9355,56668,211865,627434,1000219

%N Coefficients of the expansion of:p(x,t)=(1 - x)/((1 - x*Exp[t*(1 - x)])*(1 - x*Exp[t*(1 + x)]))

%C Row sums are:

%C {1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280, 1857945600,...}

%F p(x,t)=(1 - x)/((1 - x*Exp[t*(1 - x)])*(1 - x*Exp[t*(1 + x)]))

%e {1},

%e {1, 2, 1},

%e {1, 7, 7, 9},

%e {1, 18, 39, 68, 55, 10, 1},

%e {1, 41, 181, 381, 691, 395, 215, 15},

%e {1, 88, 733, 2048, 5378, 6512, 5026, 2816, 381, 56, 1},

%e {1, 183, 2703, 10921, 34826, 71590, 78590, 76146, 34853, 11123, 1603, 21},

%e {1, 374, 9355, 56668, 211865, 627434, 1000219, 1284488, 1109403, 573546, 245337, 37724, 4299, 246, 1},

%e {1, 757, 31009, 282445, 1275829, 4828105, 10948261, 17566417, 22506403, 17850207, 11567907, 4707207, 1126119, 197667, 8919, 27},

%e {1, 1524, 99777, 1350960, 7699308, 34659024, 106620396, 214473168, 357213030, 407969912, 351650086, 236212432, 99526828, 33716944, 6116140, 587824, 47233, 1012, 1}

%t p[t_] = (1 - x)/((1 - x*Exp[t*(1 - x)])*(1 - x*Exp[t*(1 + x)]))

%t a = Table[ CoefficientList[FullSimplify[ExpandAll[n!*(( 1 - x)^(n + 1)/(2*x))*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 1, 10}]

%t Flatten[a]

%K nonn,uned

%O 1,3

%A _Roger L. Bagula_, Nov 23 2009