A171693 -id:A171693 - cp's OEIS frontend

A171694 Expansion of g.f.: 4^nn!(1-y)^(n+1)f(x, y, m), where f(x, y, m) = 2^(m+1)exp(2^mt)/((1-yexp(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

Roger L. Bagula, Dec 15 2009

			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;

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

Cf. A060187, A159041, A171692, A171693.

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 *)

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.

Edited by G. C. Greubel, Mar 29 2022

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^mt)/((1-yexp(t))(1 + (2^(m+1)-1)exp(2^m*t))), and m = 1.

Original entry on oeis.org

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

Roger L. Bagula, Dec 15 2009

			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;

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

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

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 *)

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.

Edited by G. C. Greubel, Mar 29 2022

cp's OEIS Frontend

A171694 Expansion of g.f.: 4^nn!(1-y)^(n+1)f(x, y, m), where f(x, y, m) = 2^(m+1)exp(2^mt)/((1-yexp(t))(1 + (2^(m+1)-1)exp(2^m*t))), and m = -2.

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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^mt)/((1-yexp(t))(1 + (2^(m+1)-1)exp(2^m*t))), and m = 1.

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cp's OEIS Frontend

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.

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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.

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A171694 Expansion of g.f.: 4^nn!(1-y)^(n+1)f(x, y, m), where f(x, y, m) = 2^(m+1)exp(2^mt)/((1-yexp(t))(1 + (2^(m+1)-1)exp(2^m*t))), and m = -2.

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^mt)/((1-yexp(t))(1 + (2^(m+1)-1)exp(2^m*t))), and m = 1.