%I #10 Feb 18 2024 04:33:22

%S 1,1,1,2,4,1,0,12,9,1,0,24,48,16,1,0,0,180,140,25,1,0,0,360,840,330,

%T 36,1,0,0,0,3360,2940,672,49,1,0,0,0,6720,18480,8400,1232,64,1,0,0,0,

%U 0,75600,75600,20664,2088,81,1,0,0,0,0,151200,483840,252000,45360,3330

%N Triangle: let f(t) = 1 + t + t^2 and g(t) = t + t^2, expansion of p(t) = f(t)*exp(x*g(t)).

%e {1},

%e {1, 1},

%e {2, 4, 1},

%e {0, 12, 9, 1},

%e {0, 24, 48, 16, 1},

%e {0, 0, 180, 140, 25, 1},

%e {0, 0, 360, 840, 330, 36, 1},

%e {0, 0, 0, 3360, 2940, 672, 49, 1},

%e {0, 0, 0, 6720, 18480, 8400, 1232, 64, 1},

%e {0, 0, 0, 0, 75600, 75600, 20664, 2088, 81, 1},

%e {0, 0, 0, 0, 151200, 483840, 252000, 45360, 3330, 100, 1}

%t f[t_] = 1 + t + t^2;

%t g[t_] = t + t^2;

%t p[t_] = f[t]*Exp[x*g[t]];

%t Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];

%t a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];

%t Flatten[a]

%K nonn,uned,tabl,less

%O 1,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Apr 10 2008