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%I #13 Mar 12 2014 16:37:04
%S 1,3,3,0,24,12,-30,0,180,60,0,-720,0,1440,360,2520,0,-12600,0,12600,
%T 2520,0,120960,0,-201600,0,120960,20160,-771120,0,3810240,0,-3175200,
%U 0,1270080,181440,0,-61689600,0,101606400
%N Triangle read by rows: expansion of p(x,t) = -exp(x*t)(2*(1 - 2*exp(t)) - 2*exp(t))/(1 + exp(t)), with coefficient of x^n scaled by multiplication by (n!*(n + 2)!/4).
%C I think the rows are indexed by t = 0, 1, 2, ..., and in each row we expand the polynomial in powers of x. - _N. J. A. Sloane_, Dec 14 2010
%C Row sums are 1, 6, 36, 210, 1080, 5040, 60480, 1315440, 5443200, -558835200, 718502400,...
%e {1},
%e {3, 3},
%e {0, 24, 12},
%e {-30, 0, 180, 60},
%e {0, -720, 0, 1440, 360},
%e {2520, 0, -12600, 0, 12600, 2520},
%e {0, 120960, 0, -201600, 0, 120960, 20160},
%e {-771120, 0,3810240, 0, -3175200, 0, 1270080, 181440},
%e {0, -61689600, 0, 101606400, 0, -50803200, 0, 14515200, 1814400},
%t p[t_] = -Exp[x*t](2*(1 - 2*Exp[t]) - 2*Exp[t])/(1 + Exp[t]);
%t a = Table[ CoefficientList[(n!*(n + 2)!/4)*SeriesCoefficient[
%t Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];
%t Flatten[a]
%K sign,tabl
%O 0,2
%A _Roger L. Bagula_, Dec 12 2010
%E I rewrote the definition. - _N. J. A. Sloane_, Dec 14 2010
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