|
| |
|
|
A094368
|
|
Triangle M(k,n) read by rows: coefficients of Meixner polynomials.
|
|
1
| |
|
|
1, 1, -1, 1, -5, 1, -14, 9, 1, -30, 89, 1, -55, 439, -225, 1, -91, 1519, -3429, 1, -140, 4214, -24940, 11025, 1, -204, 10038, -122156, 230481, 1, -285, 21378, -463490, 2250621, -893025, 1, -385, 41778, -1467290, 14466221, -23941125, 1, -506
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
REFERENCES
| J. Meixner, Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion, J. Lond. Math. Soc. 9 (1934), 6-13.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Meixner Polynomial of the Second Kind
D. Foata, Combinatoire des identites sur les polynomes de Meixner, Sem. Loth. de Comb. B06c (1982).
|
|
|
FORMULA
| Recurrence: M(0) = 1, M(1) = z, M(h+1) = zM(h) - h^2*M(h-1).
G.f.: exp(z*arctan(x)) / sqrt(1+x^2).
|
|
|
EXAMPLE
| z,
z^2 - 1,
z^3 - 5*z,
z^4 - 14*z^2 + 9,
z^5 - 30*z^3 + 89*z,
z^6 - 55*z^4 + 439*z^2 - 225,
z^7 - 91*z^5 + 1519*z^3 - 3429*z,
z^8 - 140*z^6 + 4214*z^4 - 24940*z^2 + 11025,
z^9 - 204*z^7 + 10038*z^5 - 122156*z^3 + 230481*z,
|
|
|
CROSSREFS
| Essentially the same as A060338.
Sequence in context: A067558 A104792 A120393 * A087727 A039807 A185263
Adjacent sequences: A094365 A094366 A094367 * A094369 A094370 A094371
|
|
|
KEYWORD
| sign,tabl
|
|
|
AUTHOR
| Ralf Stephan, Jun 03 2004
|
| |
|
|
