|
Search: id:A141753
|
|
|
| A141753 |
|
Main diagonal of A139755, the table of q-derangement numbers of type A. |
|
+0
3
|
|
| 1, 1, 2, 7, 24, 86, 313, 1157, 4325, 16303, 61856, 235917, 903620, 3473381, 13391280, 51761781, 200523644, 778342906, 3026400508, 11785538461, 45959004812, 179444813270, 701422450293, 2744562302533, 10749124666643, 42135320616531
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
FORMULA
|
a(n) = [q^n] { ([n+1]_q)! * Sum_{m=0..n+1} (-1)^m * q^(m(m-1)/2) / ([m]_q)! }; here, the q-factorial of n is denoted by ([n]_q)! = Product_{j=1..n} (1-q^j)/(1-q).
|
|
PROGRAM
|
(PARI) {a(n)=polcoeff(prod(j=1, n+1, (1-q^j)/(1-q))* sum(k=0, n+1, (-1)^k*q^(k*(k-1)/2)/if(k==0, 1, prod(j=1, k, (1-q^j)/(1-q)))), n, q)}
|
|
CROSSREFS
|
Cf. A139755, A141754.
Sequence in context: A144170 A052986 A053368 this_sequence A014300 A128086 A131824
Adjacent sequences: A141750 A141751 A141752 this_sequence A141754 A141755 A141756
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jul 05 2008
|
|
|
Search completed in 0.002 seconds
|
