A138186 - OEIS

%I #3 Oct 13 2012 14:31:44

%S 1,1,1,6,2,1,24,18,3,1,168,96,36,4,1,960,840,240,60,5,1,9360,5760,

%T 2520,480,90,6,1,70560,65520,20160,5880,840,126,7,1,806400,564480,

%U 262080,53760,11760,1344,168,8,1,7983360,7257600,2540160,786240,120960,21168

%N A triangular sequence based on expansion of the rational polynomial of A023054 as a Sheffer sequence: p(x,t)=Exp[x*t]*(1 - t^5)/((1 - t)*(1 - t^2)^2*(1 - t^3)).

%C Row sums are:

%C {1, 2, 9, 46, 305, 2106, 18217, 163094, 1700001, 18711730, 232069961};

%F p(x,t)=Exp[x*t]*(1 - t^5)/((1 - t)*(1 - t^2)^2*(1 - t^3))=Sum(P(x,n)*t^n/n!,{n,0,Infinity}); Out_n,m=n!*Coefficients(P(x,n)).

%e {1},

%e {1, 1},

%e {6, 2, 1},

%e {24, 18, 3, 1},

%e {168, 96, 36, 4, 1},

%e {960, 840, 240, 60, 5, 1},

%e {9360, 5760, 2520, 480, 90, 6, 1},

%e {70560, 65520, 20160, 5880, 840, 126, 7, 1},

%e {806400, 564480, 262080, 53760, 11760, 1344, 168, 8, 1},

%e {7983360, 7257600, 2540160, 786240, 120960, 21168, 2016, 216, 9, 1},

%e {105235200, 79833600, 36288000, 8467200, 1965600, 241920, 35280, 2880, 270, 10, 1}

%t p[t_] = Exp[x*t]*(1 - t^5)/((1 - t)*(1 - t^2)^2*(1 - t^3)) Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]

%Y Cf. A023054.

%K nonn,uned,tabl

%O 1,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, May 04 2008