Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Mar 31 2022 13:40:39
%S 1,1,1,-1,6,-1,-1,7,25,-7,10,-44,152,-20,-2,-26,198,-292,1628,-642,94,
%T -154,1000,-1954,6416,1586,-1400,266,1646,-13606,51774,-75094,175226,
%U -73890,15962,-1378,1000,-3936,-4448,190432,37104,779104,-472160,133152,-15128
%N Expansion of g.f.: 2^(floor((n+1)/2))*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 = 1.
%H G. C. Greubel, <a href="/A171695/b171695.txt">Rows n = 0..40 of the triangle, flattened</a>
%F G.f.: 2^(floor((n+1)/2))*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 = 1.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e -1, 6, -1;
%e -1, 7, 25, -7;
%e 10, -44, 152, -20, -2;
%e -26, 198, -292, 1628, -642, 94;
%e -154, 1000, -1954, 6416, 1586, -1400, 266;
%e 1646, -13606, 51774, -75094, 175226, -73890, 15962, -1378;
%e 1000, -3936, -4448, 190432, 37104, 779104, -472160, 133152, -15128;
%t m= 1;
%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[2^(Floor[(n+1)/2])*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, A171694.
%K sign,tabl
%O 0,5
%A _Roger L. Bagula_, Dec 15 2009
%E Edited by _G. C. Greubel_, Mar 29 2022