|
Search: id:A138169
|
|
|
| A138169 |
|
Triangular sequence from the expansion of the Green's function of a vibrator: p(x,t)=Exp[x*t]/(x - t/2 - t/(Exp[t] - 1)). |
|
+0
1
|
|
| 1, 0, -2, 2, -1, 1, 6, -12, 6, 0, 12, -24, -12, 72, -72, 24, 24, -52, -88, 356, -240, -360, 720, -480, 120, 0, -720, 2280, -1320, -3720, 6360, -1200, -6000, 7200, -3600, 720, -3060, 10260, 2580, -56340, 86760, -12480, -95760, 93240, 12600, -88200, 75600, -30240, 5040, 0, 171360, -745920, 994560, 383040
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Row Sums are:{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
|
|
REFERENCES
|
Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco, 1965 page 273.
A. Messiah, Quantum Mechanics, vol. 2, p. 712, North Holland, 1969.
|
|
FORMULA
|
p(x,t)=Exp[x*t]/(x - t/2 - t/(Exp[t] - 1))=Sum(P(x,n)*t^n/n!,{n,0,Infinity}]; Out_n,m=(n+1)!*n!*Coefficients( (x-1)^(n+1)*P(x,n)).
|
|
EXAMPLE
|
{1},
{0, -2, 2},
{-1, 1, 6, -12, 6},
{0, 12, -24, -12,72, -72, 24},
{24, -52, -88, 356, -240, -360,720, -480, 120},
{0, -720, 2280, -1320, -3720, 6360, -1200, -6000, 7200, -3600, 720},
{-3060, 10260, 2580, -56340, 86760, -12480, -95760, 93240, 12600, -88200, 75600, -30240, 5040},
{0, 171360, -745920, 994560, 383040, -2462880, 2358720, 201600, -2022720, 1223040, 564480, -1270080, 846720, -282240, 40320},
{1249920, -5677056, 4185216, 23365440, -62858880, 52012800, 24748416, -82990656, 54552960, 13426560, -38949120, 14394240, 13547520, -18627840, 10160640, -2903040, 362880},
{0, -112492800, 623427840, -1257742080, 625242240, 1775571840, -3510501120, 2048820480, 1129645440, -2443271040, 1158312960, 440536320, -716325120, 137168640, 283046400, -283046400, 130636800, -32659200,3628800},
{-1253750400, 7185628800, -11222366400, -17286091200, 90010569600, -131803459200, 50190840000, 101414376000, -158091091200, 69158880000, 43010352000, -66900556800,23471078400, 11895206400, -12853209600, 439084800, 5688144000, -4490640000, 1796256000, -399168000, 39916800}
|
|
MATHEMATICA
|
Clear[p, b, a]; p[t_] = FullSimplify[Exp[x*t]/(x - t/2 - t/(Exp[t] - 1))]; Table[ ExpandAll[FullSimplify[ExpandAll[(n + 1)!n!*(x - 1)^(n + 1)*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]]]], {n, 0, 10}]; a = Table[ CoefficientList[FullSimplify[(n + 1)!n!*(x - 1)^(n + 1)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], x], {n, 0, 10}]; Flatten[a]
|
|
CROSSREFS
|
Sequence in context: A129177 A127452 A135879 this_sequence A139331 A090441 A107876
Adjacent sequences: A138166 A138167 A138168 this_sequence A138170 A138171 A138172
|
|
KEYWORD
|
nonn,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 04 2008
|
|
|
Search completed in 0.002 seconds
|
