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A171695
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.
2
1, 1, 1, -1, 6, -1, -1, 7, 25, -7, 10, -44, 152, -20, -2, -26, 198, -292, 1628, -642, 94, -154, 1000, -1954, 6416, 1586, -1400, 266, 1646, -13606, 51774, -75094, 175226, -73890, 15962, -1378, 1000, -3936, -4448, 190432, 37104, 779104, -472160, 133152, -15128
OFFSET
0,5
FORMULA
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.
EXAMPLE
Triangle begins as:
1;
1, 1;
-1, 6, -1;
-1, 7, 25, -7;
10, -44, 152, -20, -2;
-26, 198, -292, 1628, -642, 94;
-154, 1000, -1954, 6416, 1586, -1400, 266;
1646, -13606, 51774, -75094, 175226, -73890, 15962, -1378;
1000, -3936, -4448, 190432, 37104, 779104, -472160, 133152, -15128;
MATHEMATICA
m= 1;
f[t_, y_, m_]= 2^(m+1)*Exp[2^m*t]/((1-y*Exp[t])*(1+(2^(m+1)-1)*Exp[2^m*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 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Dec 15 2009
EXTENSIONS
Edited by G. C. Greubel, Mar 29 2022
STATUS
approved