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%I #10 Jun 16 2015 12:52:47
%S 8,-4,16,-20,48,32,-46,-216,336,64,-124,-1328,288,1408,128,1306,-4920,
%T -15280,9920,4800,256,17726,792,-109200,-49600,72000,14592,512,164321,
%U 467572,-407736,-1365280,243040,362880,41216,1024,627364,6599760
%N Triangle T(n,k): the coefficient of [t^n] [x^k] of 2^(n+5) *n! *exp(t*(1+t)*x) / (3+exp(t*(1+t))).
%C Row sums are 8, 12, 60, 138, 372, -3918, -53178, -492963, -1882092, 33032874, 953238882, ....
%e 8;
%e -4, 16;
%e -20, 48, 32;
%e -46, -216, 336, 64;
%e -124, -1328, 288, 1408, 128;
%e 1306, -4920, -15280, 9920, 4800, 256;
%e 17726, 792, -109200, -49600, 72000, 14592, 512;
%e 164321, 467572, -407736, -1365280, 243040, 362880, 41216, 1024;
%e 627364, 6599760, 3829280, -10328192, -8238720, 4003328, 1512448, 110592, 2048;
%e -11010958, 58617000, 126728208, -16166976, -144777024, -15660288, 29428224, 5584896, 285696, 4096;
%p A178603 := proc(n,k)
%p 2^(n+5)*n!*exp(t*(1+t)*x)/(3+exp(t*(1+t))) ;
%p coeftayl(%,t=0,n) ;
%p coeftayl(%,x=0,k) ;
%p end proc: # _R. J. Mathar_, Jun 16 2015
%t p[t_] = 4*Exp[(t + t^2)*x] /(3 + Exp[t + t^2]);
%t a = Table[ CoefficientList[FullSimplify[ExpandAll[2^(n + 3)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}];
%t Flatten[a]
%o (PARI) T(n,k)=my(t='t,x='x);polcoeff(polcoeff(2^(n+5)*n!*exp(t*(1+t)*x)/(3+exp(t*(1+t))),k,x),n,t) \\ _Charles R Greathouse IV_, Jun 16 2015
%K sign,tabl,less
%O 0,1
%A _Roger L. Bagula_, May 30 2010
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