This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171694 #7 Mar 30 2022 06:35:32 %S A171694 1,2,2,6,20,6,26,154,190,14,150,1160,3428,1352,54,1082,9174,50404, %T A171694 51724,10434,62,9366,78476,683962,1376232,734122,65996,966,94586, %U A171694 735410,9096210,30488714,32703374,8931318,530534,-4786,1091670,7562000,122859048,611454960,1132022084,653476464,111158184,2715536,71574 %N A171694 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 A171694 G. C. Greubel, <a href="/A171694/b171694.txt">Rows n = 0..40 of the triangle, flattened</a> %F A171694 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 A171694 Triangle begins as: %e A171694 1; %e A171694 2, 2; %e A171694 6, 20, 6; %e A171694 26, 154, 190, 14; %e A171694 150, 1160, 3428, 1352, 54; %e A171694 1082, 9174, 50404, 51724, 10434, 62; %e A171694 9366, 78476, 683962, 1376232, 734122, 65996, 966; %e A171694 94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786; %t A171694 m= -2; %t A171694 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 A171694 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 A171694 Cf. A060187, A159041, A171692, A171693. %K A171694 sign,tabl %O A171694 0,2 %A A171694 _Roger L. Bagula_, Dec 15 2009 %E A171694 Edited by _G. C. Greubel_, Mar 29 2022