A137369 Triangle read by rows: expansion of p(t) = (1 + t)^x/(1 + (1 + t)^n) with weight factor 2^(n+1)*n!.

1, -1, 2, 4, -12, 4, 30, 88, -60, 8, -1344, 224, 752, -224, 16, -16920, -31232, 0, 4320, -720, 32, 2977920, -430848, -371264, -10560, 19840, -2112, 64, 53267760, 104934912, -5789056, -3084928, -101920, 78848, -5824, 128, -24148131840, 1882583040, 1867684864, -54942720, -20344576, -645120, 283136

Offset

1,3

Links

Table of n, a(n) for n=1..43.

Eric Weisstein's World of Mathematics, Boole Polynomial.

Example

{1},
{-1, 2},
{4, -12, 4},
{30, 88, -60, 8},
{-1344, 224, 752, -224, 16},
{-16920, -31232,0, 4320, -720, 32},
{2977920, -430848, -371264, -10560, 19840, -2112, 64},
{53267760, 104934912, -5789056, -3084928, -101920, 78848, -5824, 128},

Mathematica

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

Crossrefs

Sequence in context: A075554 A365000 A294103 * A334766 A336847 A338118

Adjacent sequences: A137366 A137367 A137368 * A137370 A137371 A137372

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Apr 09 2008

Status

approved