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A171693
Expansion of g.f.: 2^(1+floor(n/2))*n!*((1-y)^(n+1)/(1+y))*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 = 0.
3
1, -1, 14, -1, 4, -16, 504, -16, 4, -34, 372, 2178, 35288, 2178, 372, -34, 496, -5888, 65728, 749824, 4185760, 749824, 65728, -5888, 496, -11056, 154912, -767856, 23350656, 230640288, 770603712, 230640288, 23350656, -767856, 154912, -11056
OFFSET
0,3
FORMULA
G.f.: 2^(1+floor(n/2))*n!*((1-y)^(n+1)/(1+y))*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 = 0.
EXAMPLE
Irregular triangle begins as:
1;
-1, 14, -1;
4, -16, 504, -16, 4;
-34, 372, 2178, 35288, 2178, 372, -34;
496, -5888, 65728, 749824, 4185760, 749824, 65728, -5888, 496;
MATHEMATICA
m= 0;
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[n_]:= T[n]= CoefficientList[2^(1+Floor[n/2])*n!*(1-y)^(n+1)/(1 + y)*SeriesCoefficient[Series[f[t, y, m], {t, 0, 20}], n], y];
Table[T[2*n+1], {n, 0, 12}]//Flatten (* modified by G. C. Greubel, Mar 30 2022 *)
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Roger L. Bagula, Dec 15 2009
EXTENSIONS
Edited by G. C. Greubel, Mar 31 2022
STATUS
approved