login
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.
3
1, 2, 2, 6, 20, 6, 26, 154, 190, 14, 150, 1160, 3428, 1352, 54, 1082, 9174, 50404, 51724, 10434, 62, 9366, 78476, 683962, 1376232, 734122, 65996, 966, 94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786, 1091670, 7562000, 122859048, 611454960, 1132022084, 653476464, 111158184, 2715536, 71574
OFFSET
0,2
FORMULA
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.
EXAMPLE
Triangle begins as:
1;
2, 2;
6, 20, 6;
26, 154, 190, 14;
150, 1160, 3428, 1352, 54;
1082, 9174, 50404, 51724, 10434, 62;
9366, 78476, 683962, 1376232, 734122, 65996, 966;
94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786;
MATHEMATICA
m= -2;
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[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 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Dec 15 2009
EXTENSIONS
Edited by G. C. Greubel, Mar 29 2022
STATUS
approved