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.

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

Author

Roger L. Bagula, Dec 15 2009

Keywords

• sign
• tabl

Examples

			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;
		

Links

• G. C. Greubel, Rows n = 0..40 of the triangle, flattened

Crossrefs

Cf. A060187, A159041, A171692, A171693, A171694.

Programs

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 *)

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.

Extensions

Edited by G. C. Greubel, Mar 29 2022