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%I #3 Oct 13 2012 14:33:41
%S 1,6,1,48,12,1,480,144,18,1,5760,1920,288,24,1,80640,28800,4800,480,
%T 30,1,1290240,483840,86400,9600,720,36,1,23224320,9031680,1693440,
%U 201600,16800,1008,42,1,464486400,185794560,36126720,4515840,403200,26880,1344
%N A triangular sequence based on expansion of the rational polynomial of A001788 as a Sheffer sequence: p(x,t)=Exp[x*t]*(-1/(2*t - 1)^3).
%C Row sums are:
%C {1, 7, 61, 643, 7993, 114751, 1870837, 34168891, 691354993, 15354462583,371417174701};
%F p(x,t)=Exp[x*t]*(-1/(2*t - 1)^3)=Sum(P(x,n)*t^n/n!,{n,0,Infinity}); Out_n,m=n!*Coefficients(P(x,n)).
%e {1},
%e {6, 1},
%e {48, 12, 1},
%e {480, 144, 18, 1},
%e {5760, 1920, 288, 24, 1},
%e {80640, 28800, 4800, 480, 30, 1},
%e {1290240, 483840, 86400, 9600, 720, 36, 1},
%e {23224320, 9031680, 1693440, 201600, 16800, 1008, 42, 1},
%e {464486400, 185794560, 36126720, 4515840, 403200, 26880, 1344, 48, 1}, {10218700800, 4180377600, 836075520, 108380160, 10160640, 725760, 40320,1728,54, 1},
%e {245248819200, 102187008000, 20901888000, 2786918400, 270950400, 20321280, 1209600, 57600, 2160, 60, 1}
%t p[t_] = Exp[x*t]*(-1/(2*t - 1)^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. A001788.
%K nonn,uned,tabl
%O 1,2
%A _Roger L. Bagula_ and _Gary W. Adamson_, May 04 2008
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