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%I #7 Mar 30 2022 06:35:32
%S 1,2,2,6,20,6,26,154,190,14,150,1160,3428,1352,54,1082,9174,50404,
%T 51724,10434,62,9366,78476,683962,1376232,734122,65996,966,94586,
%U 735410,9096210,30488714,32703374,8931318,530534,-4786,1091670,7562000,122859048,611454960,1132022084,653476464,111158184,2715536,71574
%N Expansion of g.f.: 4^n*n!*(1-y)^(n+1)*f(x, y, m), where f(x, y, m) = 2^(m+1)*exp(2^m*t)/((1-y*exp(t))*(1 + (2^(m+1)-1)*exp(2^m*t))), and m = -2.
%H G. C. Greubel, <a href="/A171694/b171694.txt">Rows n = 0..40 of the triangle, flattened</a>
%F G.f.: 4^n*n!*(1-y)^(n+1)*f(x, y, m), where f(x, y, m) = 2^(m+1)*exp(2^m*t)/((1-y*exp(t))*(1 + (2^(m+1)-1)*exp(2^m*t))), and m = -2.
%e Triangle begins as:
%e 1;
%e 2, 2;
%e 6, 20, 6;
%e 26, 154, 190, 14;
%e 150, 1160, 3428, 1352, 54;
%e 1082, 9174, 50404, 51724, 10434, 62;
%e 9366, 78476, 683962, 1376232, 734122, 65996, 966;
%e 94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786;
%t m= -2;
%t f[t_, y_, m_]= 2^(m+1)*Exp[2^m*t]/((1-y*Exp[t])*(1+(2^(m+1)-1)*Exp[2^m*t]));
%t Table[CoefficientList[4^n*n!*(1-y)^(n+1)*SeriesCoefficient[Series[f[t,y,m], {t,0,20}], n], y], {n,0,12}]//Flatten (* modified by _G. C. Greubel_, Mar 29 2022 *)
%Y Cf. A060187, A159041, A171692, A171693.
%K sign,tabl
%O 0,2
%A _Roger L. Bagula_, Dec 15 2009
%E Edited by _G. C. Greubel_, Mar 29 2022
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