|
Search: id:A137513
|
|
|
| A137513 |
|
Triangle read by rows: coefficients of the expansion of a polynomial related to the Poisson kernel: p(t,r)=((1 + t)/(1 - t))^x: r*Exp(i*theta)->t. |
|
+0
1
|
|
| 1, 0, 2, 0, 0, 4, 0, 4, 0, 8, 0, 0, 32, 0, 16, 0, 48, 0, 160, 0, 32, 0, 0, 736, 0, 640, 0, 64, 0, 1440, 0, 6272, 0, 2240, 0, 128, 0, 0, 33792, 0, 39424, 0, 7168, 0, 256, 0, 80640, 0, 418816, 0, 204288, 0, 21504, 0, 512, 0, 0, 2594304, 0, 3676160, 0, 924672, 0, 61440, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Row sums: {1, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600}
General relation is that Poisson's kernel is the real part of this type of function ( page 31 Hoffman reference above).
|
|
REFERENCES
|
Kenneth Hoffman and Banach Spaces of Analytic Functions, Dover, New York, 1962, page30
Thomas McCullough, Keith Phillips, Foundations of Analysis in the Complex Plane, Holt, Reinhart and Winston, New York, 1973, 215
|
|
FORMULA
|
p(t,r)=((1 + t)/(1 - t))^x: r*Exp(i*theta)->t; p(t,x)=Sum(p(x,n)&t^n/n!,{n,0,Infinity}]; Out_n,m=n!*Coefficients(P(x,n)).
|
|
EXAMPLE
|
{1},
{0, 2},
{0, 0, 4},
{0, 4, 0, 8},
{0, 0, 32, 0, 16},
{0, 48, 0, 160, 0, 32},
{0, 0, 736, 0, 640, 0, 64},
{0, 1440, 0, 6272, 0, 2240, 0, 128},
{0, 0, 33792, 0, 39424, 0, 7168, 0, 256},
{0, 80640, 0, 418816, 0, 204288, 0, 21504, 0, 512}, {0, 0, 2594304, 0, 3676160,0, 924672, 0, 61440, 0, 1024}
|
|
MATHEMATICA
|
Clear[p, f, g] p[t_] = ((1 + t)/(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
|
Sequence in context: A077959 A022002 A084658 this_sequence A140668 A071390 A061669
Adjacent sequences: A137510 A137511 A137512 this_sequence A137514 A137515 A137516
|
|
KEYWORD
|
nonn,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 23 2008
|
|
|
Search completed in 0.002 seconds
|
