A171770 Coefficients of expansion of:p(t,y)=-Exp[t/4]/(-2 + y*Exp[t/4] + y*Exp[3*t/4])

1, -1, -1, 1, 7, -1, -32, -17, 2, 1, 131, 263, -11, -1, -522, -2672, -782, 153, -16, 1, 2073, 22868, 23108, -2157, 187, -1, -8248, -179475, -410608, -61903, 18408, -3565, 272, 1, 32887, 1342125, 5870299, 3525859, -524187, 79087, -4151, -1, -131318

Offset

0,5

Comments

Row sums are:

{1,-2, 8, -48, 384, -3840, 46080, -645120, 10321920, -185794560, 3715891200,...}

Links

Table of n, a(n) for n=0..42.

Formula

p(t,y)=-Exp[t/4]/(-2 + y*Exp[t/4] + y*Exp[3*t/4])

The scaling function is:

s(y,n)=(1 - y)^(n + 1)*2*(-4)^n*n!

Example

{1},
{-1, -1},
{1, 7},
{-1, -32, -17, 2},
{1, 131, 263, -11},
{-1, -522, -2672, -782, 153, -16},
{1, 2073, 22868, 23108, -2157, 187},
{-1, -8248, -179475, -410608, -61903, 18408, -3565, 272},
{1, 32887, 1342125, 5870299, 3525859, -524187, 79087, -4151},
{-1, -131318, -9756650, -74354342, -98711444, -5029394, 3014698, -948050, 129877, -7936},
{1, 524789, 69743642, 873642650, 2116045028, 790707644, -166952794, 35456678, -3428005, 151567}

Mathematica

Clear[m, n, t, x, y, a]
f[t_, y_] = -Exp[t/4]/(-2 + y*Exp[t/4] + y*Exp[3*t/4]) Table[ FullSimplify[ ExpandAll[(1 - y)^(n + 1)*2*(-4)^n* n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], {n, 0, 10}]
a = Table[ CoefficientList[FullSimplify[ExpandAll[( 1 - y)^(n + 1)*2*(-4)^n*n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 0, 10}]
Flatten[a]

Crossrefs

Sequence in context: A084181 A002678 A147482 * A050402 A027643 A225122

Adjacent sequences: A171767 A171768 A171769 * A171771 A171772 A171773

Keyword

sign,uned

Author

Roger L. Bagula, Dec 18 2009

Status

approved