|
| |
|
|
A081048
|
|
Signed Stirling numbers of the first kind.
|
|
2
| |
|
|
0, 1, -3, 11, -50, 274, -1764, 13068, -109584, 1026576, -10628640, 120543840, -1486442880, 19802759040, -283465647360, 4339163001600, -70734282393600, 1223405590579200, -22376988058521600, 431565146817638400, -8752948036761600000, 186244810780170240000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
FORMULA
| a(n)=n!*Sum {k=1..n, (-1)^(n+1)*1/k} E.g.f. (1+x)^-1 * log(1+x).
|
|
|
EXAMPLE
| a(9): coefficient of p^2 in polynomial p (p - 1) (p - 2) (p - 3) (p - 4) (p - 5) (p - 6) (p - 7) (p - 8) = -1 + 40320 p - 109584 p^2 + 118124 p^3 - 67284 p^4 + 22449 p^5 - 4536 p^6 + 546 p^7 - 36 p^8 + p^9 is equal to -109584. [From Artur Jasinski (grafix(AT)csl.pl), Nov 30 2008]
|
|
|
MATHEMATICA
| aa = {}; Do[AppendTo[aa, Coefficient[Expand[Product[p - n, {n, 0, m}]], p, 2]], {m, 1, 20}]; aa [From Artur Jasinski (grafix(AT)csl.pl), Nov 30 2008]
|
|
|
CROSSREFS
| Cf. A000254, A008275.
Sequence in context: A103466 A203166 A000254 * A065048 A024335 A203009
Adjacent sequences: A081045 A081046 A081047 * A081049 A081050 A081051
|
|
|
KEYWORD
| easy,sign
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 05 2003
|
| |
|
|
