|
Search: id:A089656
|
|
|
| A089656 |
|
Given a distribution of n balls, labeled 1,...,n, among n unlabeled contents-ordered urns, arrange the nonempty urns in increasing order of their initial elements: U_1,...U_k, and sum the quantities (i-1)(card U_i - 1) for i=1,...,k to get the "weight" of this distribution. These numbers represent the number of distributions of even weight minus the number with odd weight. |
|
+0
1
|
|
| 1, 1, 3, 7, 41, 161, 1387, 7687, 86865, 623233, 8682131, 76586951, 1265108473
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
Mark A. Shattuck and Carl G. Wagner, Parity Theorems for Statistics on Lattice Paths and Laguerre Distributions, Research Report, Mathematics Department, University of Tennessee, Knoxville, TN, 2004
Mark A. Shattuck and Carl G. Wagner, Parity Theorems for Statistics on Lattice Paths and Laguerre Configurations, Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.1.
|
|
FORMULA
|
E.g.f.: cosh(x*(1-x^2)^-1/2) + (1-x^2)^1/2*(1-x)^-1*sinh(x*(1-x^2)^-1/2)
|
|
EXAMPLE
|
a(3)=7 because there are 9 distributions of balls 1,2,3 with weight 0: 123,132,213,231,312,321,12-3,13-2, and 1-2-3, and 2 distributions of weight 1:1-23 and 1-32 (dashes separate contents-ordered urns)
|
|
CROSSREFS
|
Sequence in context: A071730 A058815 A138901 this_sequence A018970 A018968 A018969
Adjacent sequences: A089653 A089654 A089655 this_sequence A089657 A089658 A089659
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Carl G. Wagner (wagner(AT)math.utk.edu), Jan 15 2004
|
|
|
Search completed in 0.002 seconds
|
