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A137387 Triangular sequence from coefficients of the expansion of p(x,t)=Exp[2*x*t]*t/(1 - t).

%I A137387 #2 Mar 30 2012 17:34:26
%S A137387 0,1,2,4,6,12,12,24,48,48,32,120,240,240,160,80,720,1440,1440,960,480,
%T A137387 192,5040,10080,10080,6720,3360,1344,448,40320,80640,80640,53760,
%U A137387 26880,10752,3584,1024,362880,725760,725760,483840,241920,96768,32256,9216
%N A137387 Triangular sequence from coefficients of the expansion of p(x,t)=Exp[2*x*t]*t/(1 - t).
%C A137387 Row sums = A066534.
%D A137387 Terrell Hill, Statistical Mechanics, Dover, 1987, page 417
%F A137387 p(x,t)=Exp[2*x*t]*t/(1 - t)=Sum[P(x,n)*t6n/n!,{n,1,Infinity}]; out_n,m=n!*Coefficients(P(x,n)).
%e A137387 {0},
%e A137387 {1},
%e A137387 {2, 4},
%e A137387 {6, 12, 12},
%e A137387 {24, 48, 48, 32},
%e A137387 {120, 240, 240, 160, 80},
%e A137387 {720, 1440, 1440, 960, 480, 192},
%e A137387 {5040, 10080, 10080, 6720, 3360, 1344, 448},
%e A137387 {40320, 80640, 80640, 53760, 26880, 10752, 3584, 1024},
%e A137387 {362880, 725760, 725760, 483840, 241920, 96768, 32256, 9216, 2304},
%e A137387 {3628800, 7257600, 7257600, 4838400, 2419200, 967680, 322560, 92160, 23040,5120}
%t A137387 p[t_] = Exp[2*x*t]*t/(1 - t); Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
%Y A137387 Cf. A066534.
%K A137387 nonn,tabl
%O A137387 1,3
%A A137387 _Roger L. Bagula_, Apr 26 2008