A168347 Coefficients of the expansion of:p(x,t)=(1 - x)/((1 - x*Exp[t*(1 - x)])*(1 - x*Exp[t*(1 + x)]))

1, 1, 2, 1, 1, 7, 7, 9, 1, 18, 39, 68, 55, 10, 1, 1, 41, 181, 381, 691, 395, 215, 15, 1, 88, 733, 2048, 5378, 6512, 5026, 2816, 381, 56, 1, 1, 183, 2703, 10921, 34826, 71590, 78590, 76146, 34853, 11123, 1603, 21, 1, 374, 9355, 56668, 211865, 627434, 1000219

Offset

1,3

Comments

Row sums are:

{1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280, 1857945600,...}

Links

Table of n, a(n) for n=1..53.

Formula

p(x,t)=(1 - x)/((1 - x*Exp[t*(1 - x)])*(1 - x*Exp[t*(1 + x)]))

Example

{1},
{1, 2, 1},
{1, 7, 7, 9},
{1, 18, 39, 68, 55, 10, 1},
{1, 41, 181, 381, 691, 395, 215, 15},
{1, 88, 733, 2048, 5378, 6512, 5026, 2816, 381, 56, 1},
{1, 183, 2703, 10921, 34826, 71590, 78590, 76146, 34853, 11123, 1603, 21},
{1, 374, 9355, 56668, 211865, 627434, 1000219, 1284488, 1109403, 573546, 245337, 37724, 4299, 246, 1},
{1, 757, 31009, 282445, 1275829, 4828105, 10948261, 17566417, 22506403, 17850207, 11567907, 4707207, 1126119, 197667, 8919, 27},
{1, 1524, 99777, 1350960, 7699308, 34659024, 106620396, 214473168, 357213030, 407969912, 351650086, 236212432, 99526828, 33716944, 6116140, 587824, 47233, 1012, 1}

Mathematica

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

Crossrefs

Sequence in context: A128596 A176305 A139349 * A120475 A086738 A351083

Adjacent sequences: A168344 A168345 A168346 * A168348 A168349 A168350

Keyword

nonn,uned

Author

Roger L. Bagula, Nov 23 2009

Status

approved