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.

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

Links

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

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

Cf. A060187, A159041, A171692, A171693.

Sequence in context: A233113 A366731 A341380 * A103179 A320932 A225942

Adjacent sequences: A171691 A171692 A171693 * A171695 A171696 A171697

Keyword

sign,tabl

Author

Roger L. Bagula, Dec 15 2009

Extensions

Edited by G. C. Greubel, Mar 29 2022

Status

approved