A171721 Coefficient expansion of: f(t,y)=((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t])

1, 1, 3, 2, 3, 7, 17, 17, 7, 15, 116, 122, 116, 15, 31, 627, 1262, 1262, 627, 31, 63, 2990, 12433, 15108, 12433, 2990, 63, 127, 13309, 107151, 201973, 201973, 107151, 13309, 127, 255, 56936, 830628, 2612184, 3321914, 2612184, 830628, 56936, 255, 511

Offset

1,3

Comments

Row sums are:

2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560, 3715891200,...

Links

Table of n, a(n) for n=1..45.

Formula

f(t,y)=((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t])

Example

{1, 1},
{3, 2, 3},
{7, 17, 17, 7},
{15, 116, 122, 116, 15},
{31, 627, 1262, 1262, 627, 31}, {63, 2990, 12433, 15108, 12433, 2990, 63},
{127, 13309, 107151, 201973, 201973, 107151, 13309, 127},
{255, 56936, 830628, 2612184, 3321914, 2612184, 830628, 56936, 255},
{511, 237863, 5979980, 30947132, 55731794, 55731794, 30947132, 5979980, 237863, 511},
{1023, 979298, 40909331, 336803864, 900995822, 1156512524, 900995822, 336803864, 40909331, 979298, 1023}

Mathematica

f[t_, y_] = ((1 + y)/y - Exp[t/2])/(-1 + y*Exp[t]);
a = Table[ CoefficientList[FullSimplify[ExpandAll[(-1 + y)^(n + 1)*(-2)^n*n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 1, 10}]
Flatten[a]

Crossrefs

Sequence in context: A274508 A347112 A227104 * A225695 A226469 A073341

Adjacent sequences: A171718 A171719 A171720 * A171722 A171723 A171724

Keyword

nonn,uned

Author

Roger L. Bagula, Dec 16 2009

Status

approved