OFFSET
1,6
COMMENTS
Row sums: {0, 0, 0, 0, 0, 24, 360, 2520, 0, -169344, 0};
These functions are due to the close connection of the Bernoulli-type functions with the Zeta (generalized) functions.
FORMULA
Zeta[6,1+1/t-x] = Sum[1/(n+1/t+x)^6,{n,0,Infinity}] = Sum[p(x,n)*t^n/n!,{n,0,Infinity}]; out(n,m)=n!*Coefficients(p(x,n)).
EXAMPLE
{0},
{0},
{0},
{0},
{0},
{24},
{-360,720},
{2520, -15120, 15120},
{0, 141120, -423360, 282240},
{-169344, 0, 5080320, -10160640, 5080320},
{0, -15240960, 0, 152409600, -228614400, 91445760}
MATHEMATICA
LaplaceTransform[t*Exp[x*t]/(Exp[t] - 1), t, s]; Clear[p, f, g] p[t_] = Zeta[6, 1 + 1/t - x]; Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ FullSimplify[Series[p[t], {t, 0, 30}]], n], x], {n, 0, 10}]; Flatten[a]
CROSSREFS
KEYWORD
uned,tabf,sign
AUTHOR
Roger L. Bagula, Apr 22 2008
STATUS
approved