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.

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

Links

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

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

Cf. A060187, A159041, A171692, A171694, A171695.

Sequence in context: A040204 A040203 A040205 * A235704 A229199 A040206

Adjacent sequences: A171690 A171691 A171692 * A171694 A171695 A171696

Keyword

sign,tabf

Author

Roger L. Bagula, Dec 15 2009

Extensions

Edited by G. C. Greubel, Mar 31 2022

Status

approved