|
| |
|
|
A078521
|
|
Signed triangle of D'Arcais numbers (A008298) : coefficients of r in the polynomials generated by the series coefficients of z^n in Product[(1-z^k)^r, {k,1,Inf}]*(n!).
|
|
0
| |
|
|
1, 0, -1, 0, -3, 1, 0, -8, 9, -1, 0, -42, 59, -18, 1, 0, -144, 450, -215, 30, -1, 0, -1440, 3394, -2475, 565, -45, 1, 0, -5760, 30912, -28294, 9345, -1225, 63, -1, 0, -75600, 293292, -340116, 147889, -27720, 2338, -84, 1, 0, -524160, 3032208, -4335596, 2341332, -579369, 69552, -4074, 108, -1, 0, -6531840
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| Row sums give A010815 * n!.
|
|
|
FORMULA
| See Mathematica line
|
|
|
EXAMPLE
| The z-expansion of Product[(1-z^k)^r, {k,1,3}] is 1 - r*z + ((-3+r)*r*z^2)/2 -(r*(8-9*r +r^2)*z^3)/6, so the third row of the triangle is 0,-8,9,-1.
Triangle begins
1,
0, -1,
0, -3, 1,
0, -8, 9, -1,
0, -42, 59, -18, 1,
0, -144, 450, -215, 30, -1,
0, -1440, 3394, -2475, 565, -45, 1,
0, -5760, 30912, -28294, 9345, -1225, 63, -1,
0, -75600, 293292, -340116, 147889, -27720, 2338, -84, 1
...
|
|
|
MATHEMATICA
| w=16; (CoefficientList[ #, r]&/@ CoefficientList[Series[Product[(1-z^k)^r, {k, 1, w}], {z, 0, w}], z])Range[0, w]!
|
|
|
CROSSREFS
| Cf. A010815, A008298.
Sequence in context: A187557 A052420 A162971 * A194938 A135871 A126178
Adjacent sequences: A078518 A078519 A078520 * A078522 A078523 A078524
|
|
|
KEYWORD
| easy,sign,tabl
|
|
|
AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jan 07 2003
|
| |
|
|
